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friends! I've never worked with matrices in Mathematica before so I'm asking for some help.

I have to find determinant of such matrix 100x100.. How can I do that? enter image description here

Thanks a lot for advices!

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n = 10;
sa1 = SparseArray[{Band[{1, 1}] -> a, Band[{2, 1}, {n, n}] -> {b, c}, 
    Band[{1, 2}, {n, n}] -> {b, c}}, {n, n}];
MatrixForm[sa1]

Mathematica graphics

Det@sa1

Mathematica graphics

FullSimplify@Det@sa1

Mathematica graphics

sa2 = SparseArray[{Band[{1, 1}] -> a, Band[{2, 1}, {n, n}] -> {b, b, c, c}, 
    Band[{1, 2}, {n, n}] -> {b, b, c, c}}, {n, n}];
MatrixForm[sa2]

Mathematica graphics

Det@sa2

Mathematica graphics

FullSimplify@Det@sa2

Mathematica graphics

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