# Manipulating ParametricPlot

I have to solve the following task: Write a Manipulate command containing the values ​​a, b, c and d of the matrix $$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$$ each varied in the range [0,1]. Start with a and d at value 1 and b unch c at value 0. In the manipulate environment, plot the values ​​of all unit vectors after applying the matrix in a parametric plot. I wrote the following:

MatrixForm [M = {a, b}, {c, d}]
Manipulate [
ParametricPlot [
M. {Cos [\ Phi], Sin [\ Phi]}, {\ Phi, 0, 2 Pi},
PlotRange -> {{-1.4, 1.4}, {-1.4, 1.4}}], {{a, 1, "a"}, 0,
1}, {{b, 0, "b"}, 0, 1}, {{c, 0, "c"}, 0, 1}, {{d, 1, "d"}, 0, 1} ]


But it does not work. Can you help me? Thank you

Maniputate wants to see its variables explicitly in the expressions. This should work:
M = {a, b, c, d} \[Function] {{a, b}, {c, d}};