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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