# Inverse matrix

Algebra Level 4

If matrix $$A=\begin{pmatrix} a & b \\ c & a \end{pmatrix}$$ satisfies $$A={A}^{-1},$$ what are all possible values of real number $$x$$ such that the matrix $$A-xI$$ is not invertible?

Details and assumptions

$$I$$ denotes the identity matrix.

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