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I am solving an $11\times11$ matrix in Mathematica. I am facing problem when I try to find the determinant or eigenvalues of this matrix. The error (Det::matsq/Eigenvalues::matsq) generated shows that the matrix is not square therefore it cannot solve it. But when I manually check the matrix by checking the dimension it gives $11\times11$ matrix.

Another issue that I am facing is that when I ask the logical question from Mathematica to check whether my matrix is symmetric or not? Mathematica always give false. Whereas, again when I manually check the solution by subtracting the matrix from its transpose, I get a $11\times11$ null matrix.

So far these things are making me very confused, a help from your end will be highly appreciated. I am also attaching the program with this email.

ClearAll["Global`*"]
KLC = {{{(47 C55c)/(30 c) + (6 c (b^2 C11c + a^2 C66c) π^2)/(
      35 a^2 b^2) + (C11t/a^2 + C66t/b^2) ft π^2}, {-((7 C55c)/(
       30 c)) + (c (b^2 C11c + a^2 C66c) π^2)/(
      35 a^2 b^2)}, {-((4 C55c)/(3 c)) + (
      2 c (b^2 C11c + a^2 C66c) π^2)/(15 a^2 b^2)}, {2/
      35 (-14 C55c + 
        c^2 (C11c/a^2 + C66c/b^2) π^2)}, {((6 c (C12c + C66c) + 
        35 (C12t + C66t) ft) π^2)/(35 a b)}, {(
     c (C12c + C66c) π^2)/(35 a b)}, {(
     2 c (C12c + C66c) π^2)/(
     15 a b)}, {-((2 c^2 (C12c + C66c) π^2)/(
      35 a b))}, {((-22 c C13c + 38 c C55c + 47 C55c ft) π)/(
      60 a c) + (3 c (b^2 C11c + a^2 (C12c + 2 C66c)) ft π^3)/(
      35 a^3 b^2)}, {(π (-6 c^2 C11c fb π^2 + 
        a^2 (-14 c (C13c + C55c) + 49 C55c fb - (
           6 c^2 (C12c + 2 C66c) fb π^2)/b^2)))/(420 a^3 c)}, {(
     2 (C13c + C55c) π)/(
     5 a)}}, {{-((7 C55c)/(30 c)) + (
      c (b^2 C11c + a^2 C66c) π^2)/(35 a^2 b^2)}, {(47 C55c)/(
      30 c) + (6 c (b^2 C11c + a^2 C66c) π^2)/(
      35 a^2 b^2) + (C11b/a^2 + C66b/b^2) fb π^2}, {-((4 C55c)/(
       3 c)) + (2 c (b^2 C11c + a^2 C66c) π^2)/(15 a^2 b^2)}, {(
      4 C55c)/5 - (2 c^2 (b^2 C11c + a^2 C66c) π^2)/(
      35 a^2 b^2)}, {(c (C12c + C66c) π^2)/(
     35 a b)}, {((6 c (C12c + C66c) + 35 (C12b + C66b) fb) π^2)/(
     35 a b)}, {(2 c (C12c + C66c) π^2)/(15 a b)}, {(
     2 c^2 (C12c + C66c) π^2)/(35 a b)}, {(
     6 c^2 C11c ft π^3 + 
      a^2 π (14 c (C13c + C55c) - 49 C55c ft + (
         6 c^2 (C12c + 2 C66c) ft π^2)/b^2))/(
     420 a^3 c)}, {((22 c C13c - 38 c C55c - 47 C55c fb) π)/(
      60 a c) - (3 c (b^2 C11c + a^2 (C12c + 2 C66c)) fb π^3)/(
      35 a^3 b^2)}, {-((2 (C13c + C55c) π)/(
      5 a))}}, {{-((4 C55c)/(3 c)) + (
      2 c (b^2 C11c + a^2 C66c) π^2)/(
      15 a^2 b^2)}, {-((4 C55c)/(3 c)) + (
      2 c (b^2 C11c + a^2 C66c) π^2)/(15 a^2 b^2)}, {(8 C55c)/(
      3 c) + 16/15 c (C11c/a^2 + C66c/b^2) π^2}, {0}, {(
     2 c (C12c + C66c) π^2)/(15 a b)}, {(
     2 c (C12c + C66c) π^2)/(15 a b)}, {(
     16 c (C12c + C66c) π^2)/(15 a b)}, {0}, {(
     c^2 C11c ft π^3 + 
      a^2 π (-10 (c (C13c + C55c) + C55c ft) + (
         c^2 (C12c + 2 C66c) ft π^2)/b^2))/(
     15 a^3 c)}, {(2 (c (C13c + C55c) + C55c fb) π)/(3 a c) - (
      c (b^2 C11c + a^2 (C12c + 2 C66c)) fb π^3)/(
      15 a^3 b^2)}, {0}}, {{2/
      35 (-14 C55c + c^2 (C11c/a^2 + C66c/b^2) π^2)}, {(4 C55c)/
      5 - (2 c^2 (b^2 C11c + a^2 C66c) π^2)/(
      35 a^2 b^2)}, {0}, {8/
      105 c (21 C55c + 2 c^2 (C11c/a^2 + C66c/b^2) π^2)}, {(
     2 c^2 (C12c + C66c) π^2)/(
     35 a b)}, {-((2 c^2 (C12c + C66c) π^2)/(35 a b))}, {0}, {-((
      16 c^3 (C12c + C66c) π^2)/(
      105 a b))}, {-((2 (2 c (C13c + C55c) + 3 C55c ft) π)/(
       15 a)) + (c^2 (b^2 C11c + a^2 (C12c + 2 C66c)) ft π^3)/(
      35 a^3 b^2)}, {-((2 (2 c (C13c + C55c) + 3 C55c fb) π)/(
       15 a)) + (c^2 (b^2 C11c + a^2 (C12c + 2 C66c)) fb π^3)/(
      35 a^3 b^2)}, {(8 c (C13c + C55c) π)/(
     15 a)}}, {{((6 c (C12c + C66c) + 35 (C12t + C66t) ft) π^2)/(
     35 a b)}, {(c (C12c + C66c) π^2)/(35 a b)}, {(
     2 c (C12c + C66c) π^2)/(15 a b)}, {(
     2 c^2 (C12c + C66c) π^2)/(
     35 a b)}, {(47 C44c)/(30 c) + (
      6 c (a^2 C22c + b^2 C66c) π^2)/(
      35 a^2 b^2) + (C22t/b^2 + C66t/a^2) ft π^2}, {-((7 C44c)/(
       30 c)) + (c (a^2 C22c + b^2 C66c) π^2)/(
      35 a^2 b^2)}, {-((4 C44c)/(3 c)) + (
      2 c (a^2 C22c + b^2 C66c) π^2)/(15 a^2 b^2)}, {(4 C44c)/
      5 - (2 c^2 (a^2 C22c + b^2 C66c) π^2)/(
      35 a^2 b^2)}, {((-22 c C23c + 38 c C44c + 47 C44c ft) π)/(
      60 b c) + (3 c (a^2 C22c + b^2 (C12c + 2 C66c)) ft π^3)/(
      35 a^2 b^3)}, {(π (-6 c^2 C22c fb π^2 + 
        b^2 (-14 c (C23c + C44c) + 49 C44c fb - (
           6 c^2 (C12c + 2 C66c) fb π^2)/a^2)))/(420 b^3 c)}, {(
     2 (C23c + C44c) π)/(5 b)}}, {{(c (C12c + C66c) π^2)/(
     35 a b)}, {((6 c (C12c + C66c) + 35 (C12b + C66b) fb) π^2)/(
     35 a b)}, {(2 c (C12c + C66c) π^2)/(
     15 a b)}, {-((2 c^2 (C12c + C66c) π^2)/(
      35 a b))}, {-((7 C44c)/(30 c)) + (
      c (a^2 C22c + b^2 C66c) π^2)/(35 a^2 b^2)}, {(47 C44c)/(
      30 c) + (6 c (a^2 C22c + b^2 C66c) π^2)/(
      35 a^2 b^2) + (C22b/b^2 + C66b/a^2) fb π^2}, {-((4 C44c)/(
       3 c)) + (2 c (a^2 C22c + b^2 C66c) π^2)/(15 a^2 b^2)}, {2/
      35 (-14 C44c + c^2 (C22c/b^2 + C66c/a^2) π^2)}, {(
     6 c^2 C22c ft π^3 + 
      b^2 π (14 c (C23c + C44c) - 49 C44c ft + (
         6 c^2 (C12c + 2 C66c) ft π^2)/a^2))/(
     420 b^3 c)}, {((22 c C23c - 38 c C44c - 47 C44c fb) π)/(
      60 b c) - (3 c (a^2 C22c + b^2 (C12c + 2 C66c)) fb π^3)/(
      35 a^2 b^3)}, {-((2 (C23c + C44c) π)/(5 b))}}, {{(
     2 c (C12c + C66c) π^2)/(15 a b)}, {(
     2 c (C12c + C66c) π^2)/(15 a b)}, {(
     16 c (C12c + C66c) π^2)/(
     15 a b)}, {0}, {-((4 C44c)/(3 c)) + (
      2 c (a^2 C22c + b^2 C66c) π^2)/(
      15 a^2 b^2)}, {-((4 C44c)/(3 c)) + (
      2 c (a^2 C22c + b^2 C66c) π^2)/(15 a^2 b^2)}, {(8 C44c)/(
      3 c) + 16/15 c (C22c/b^2 + C66c/a^2) π^2}, {0}, {(
     c^2 C22c ft π^3 + 
      b^2 π (-10 (c (C23c + C44c) + C44c ft) + (
         c^2 (C12c + 2 C66c) ft π^2)/a^2))/(
     15 b^3 c)}, {(2 (c (C23c + C44c) + C44c fb) π)/(3 b c) - (
      c (a^2 C22c + b^2 (C12c + 2 C66c)) fb π^3)/(
      15 a^2 b^3)}, {0}}, {{-((2 c^2 (C12c + C66c) π^2)/(
      35 a b))}, {(2 c^2 (C12c + C66c) π^2)/(
     35 a b)}, {0}, {-((16 c^3 (C12c + C66c) π^2)/(105 a b))}, {(
      4 C44c)/5 - (2 c^2 (a^2 C22c + b^2 C66c) π^2)/(
      35 a^2 b^2)}, {2/
      35 (-14 C44c + c^2 (C22c/b^2 + C66c/a^2) π^2)}, {0}, {8/
      105 c (21 C44c + 2 c^2 (C22c/b^2 + C66c/a^2) π^2)}, {(
      2 (2 c (C23c + C44c) + 3 C44c ft) π)/(15 b) - (
      c^2 (a^2 C22c + b^2 (C12c + 2 C66c)) ft π^3)/(
      35 a^2 b^3)}, {(2 (2 c (C23c + C44c) + 3 C44c fb) π)/(
      15 b) - (c^2 (a^2 C22c + b^2 (C12c + 2 C66c)) fb π^3)/(
      35 a^2 b^3)}, {-((8 c (C23c + C44c) π)/(
      15 b))}}, {{((-22 c C13c + 38 c C55c + 47 C55c ft) π)/(
      60 a c) + (3 c (b^2 C11c + a^2 (C12c + 2 C66c)) ft π^3)/(
      35 a^3 b^2)}, {(
     6 c^2 C11c ft π^3 + 
      a^2 π (14 c (C13c + C55c) - 49 C55c ft + (
         6 c^2 (C12c + 2 C66c) ft π^2)/b^2))/(420 a^3 c)}, {(
     c^2 C11c ft π^3 + 
      a^2 π (-10 (c (C13c + C55c) + C55c ft) + (
         c^2 (C12c + 2 C66c) ft π^2)/b^2))/(
     15 a^3 c)}, {-((2 (2 c (C13c + C55c) + 3 C55c ft) π)/(
       15 a)) + (c^2 (b^2 C11c + a^2 (C12c + 2 C66c)) ft π^3)/(
      35 a^3 b^2)}, {((-22 c C23c + 38 c C44c + 47 C44c ft) π)/(
      60 b c) + (3 c (a^2 C22c + b^2 (C12c + 2 C66c)) ft π^3)/(
      35 a^2 b^3)}, {(
     6 c^2 C22c ft π^3 + 
      b^2 π (14 c (C23c + C44c) - 49 C44c ft + (
         6 c^2 (C12c + 2 C66c) ft π^2)/a^2))/(420 b^3 c)}, {(
     c^2 C22c ft π^3 + 
      b^2 π (-10 (c (C23c + C44c) + C44c ft) + (
         c^2 (C12c + 2 C66c) ft π^2)/a^2))/(
     15 b^3 c)}, {(2 (2 c (C23c + C44c) + 3 C44c ft) π)/(15 b) - (
      c^2 (a^2 C22c + b^2 (C12c + 2 C66c)) ft π^3)/(
      35 a^2 b^3)}, {1/(
      840 a^4 b^4 c) (980 a^4 b^4 C33c + 
        7 a^2 b^2 (a^2 (32 c^2 C44c + 47 C44c ft^2 - 
              4 c (11 C23c ft - 19 C44c ft + 30 ktP)) + 
           b^2 (32 c^2 C55c + 47 C55c ft^2 - 
              4 c (11 C13c ft - 19 C55c ft + 30 ktP))) π^2 + 
        2 c ft^2 (18 c (b^4 C11c + a^4 C22c + 
              2 a^2 b^2 (C12c + 2 C66c)) + 
           35 (b^4 C11t + a^4 C22t + 
              2 a^2 b^2 (C12t + 2 C66t)) ft) π^4)}, {1/(
      840 a^4 b^4 c) (140 a^4 b^4 C33c - 
        7 a^2 b^2 (a^2 (8 c^2 C44c - 7 C44c fb ft + 
              2 c (C23c + C44c) (fb + ft)) + 
           b^2 (8 c^2 C55c - 7 C55c fb ft + 
              2 c (C13c + C55c) (fb + ft))) π^2 - 
        6 c^2 (b^4 C11c + a^4 C22c + 
           2 a^2 b^2 (C12c + 2 C66c)) fb ft π^4)}, {1/
      15 (-((20 C33c)/c) + 2 c (C44c/b^2 + C55c/a^2) π^2 + 
        3 ((C23c + C44c)/b^2 + (C13c + C55c)/
           a^2) ft π^2)}}, {{(π (-6 c^2 C11c fb π^2 + 
        a^2 (-14 c (C13c + C55c) + 49 C55c fb - (
           6 c^2 (C12c + 2 C66c) fb π^2)/b^2)))/(
     420 a^3 c)}, {((22 c C13c - 38 c C55c - 47 C55c fb) π)/(
      60 a c) - (3 c (b^2 C11c + a^2 (C12c + 2 C66c)) fb π^3)/(
      35 a^3 b^2)}, {(2 (c (C13c + C55c) + C55c fb) π)/(3 a c) - (
      c (b^2 C11c + a^2 (C12c + 2 C66c)) fb π^3)/(
      15 a^3 b^2)}, {-((2 (2 c (C13c + C55c) + 3 C55c fb) π)/(
       15 a)) + (c^2 (b^2 C11c + a^2 (C12c + 2 C66c)) fb π^3)/(
      35 a^3 b^2)}, {(π (-6 c^2 C22c fb π^2 + 
        b^2 (-14 c (C23c + C44c) + 49 C44c fb - (
           6 c^2 (C12c + 2 C66c) fb π^2)/a^2)))/(
     420 b^3 c)}, {((22 c C23c - 38 c C44c - 47 C44c fb) π)/(
      60 b c) - (3 c (a^2 C22c + b^2 (C12c + 2 C66c)) fb π^3)/(
      35 a^2 b^3)}, {(2 (c (C23c + C44c) + C44c fb) π)/(3 b c) - (
      c (a^2 C22c + b^2 (C12c + 2 C66c)) fb π^3)/(15 a^2 b^3)}, {(
      2 (2 c (C23c + C44c) + 3 C44c fb) π)/(15 b) - (
      c^2 (a^2 C22c + b^2 (C12c + 2 C66c)) fb π^3)/(
      35 a^2 b^3)}, {1/(
      840 a^4 b^4 c) (140 a^4 b^4 C33c - 
        7 a^2 b^2 (a^2 (8 c^2 C44c - 7 C44c fb ft + 
              2 c (C23c + C44c) (fb + ft)) + 
           
           b^2 (8 c^2 C55c - 7 C55c fb ft + 
              2 c (C13c + C55c) (fb + ft))) π^2 - 
        6 c^2 (b^4 C11c + a^4 C22c + 
           2 a^2 b^2 (C12c + 2 C66c)) fb ft π^4)}, {1/(
      840 a^4 b^4 c) (980 a^4 b^4 C33c + 
        7 a^2 b^2 (a^2 (32 c^2 C44c + 47 C44c fb^2 - 
              4 c (11 C23c fb - 19 C44c fb + 30 ktP)) + 
           b^2 (32 c^2 C55c + 47 C55c fb^2 - 
              4 c (11 C13c fb - 19 C55c fb + 30 ktP))) π^2 + 
        2 c fb^2 (18 c (b^4 C11c + a^4 C22c + 
              2 a^2 b^2 (C12c + 2 C66c)) + 
           35 (b^4 C11b + a^4 C22b + 
              2 a^2 b^2 (C12b + 2 C66b)) fb) π^4)}, {1/
      15 (-((20 C33c)/c) + 2 c (C44c/b^2 + C55c/a^2) π^2 + 
        3 ((C23c + C44c)/b^2 + (C13c + C55c)/a^2) fb π^2)}}, {{(
     2 (C13c + C55c) π)/(
     5 a)}, {-((2 (C13c + C55c) π)/(5 a))}, {0}, {(
     8 c (C13c + C55c) π)/(15 a)}, {(2 (C23c + C44c) π)/(
     5 b)}, {-((2 (C23c + C44c) π)/(5 b))}, {0}, {-((
      8 c (C23c + C44c) π)/(15 b))}, {1/
      15 (-((20 C33c)/c) + 2 c (C44c/b^2 + C55c/a^2) π^2 + 
        3 ((C23c + C44c)/b^2 + (C13c + C55c)/a^2) ft π^2)}, {1/
      15 (-((20 C33c)/c) + 2 c (C44c/b^2 + C55c/a^2) π^2 + 
        3 ((C23c + C44c)/b^2 + (C13c + C55c)/a^2) fb π^2)}, {(
      8 C33c)/(3 c) + 16/15 c (C44c/b^2 + C55c/a^2) π^2}}};
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There are extra { } in every one of your elements as below.

matrix = {{{a}, {b}}, {{c}, {d}}};
ArrayDepth[matrix]
matrix // MatrixForm

3

So your need

Flatten /@ matrix
Flatten /@ KLC
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  • $\begingroup$ Let me check. Thank you for your help :) $\endgroup$ – Wajihuddin Qazi Nov 28 '20 at 12:31

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