Show that if `lambda_(1), lambda_(2), ...., lamnda_(n)` are `n` eigenvalues of a square matrix a of order n, then the eigenvalues of the matric `A^(2)` are `lambda_(1)^(2), lambda_(2)^(2),..., lambda_(n)^(2)`.

Explanation

`AX=lambdaX`
or `A(AX)=A(lambdaX)`
or `A^(2)X=lambda(AX)=lambda(lambdaX)=lambda^(2)X`
i.e., `A^(2)X=lambda^(2)X`
Hence, eigenvalue of `A^(2)` is `lambda^(2)`. Thus, if `lambda_(1), lambda_(2), ..., lambda_(n)` are eigenvalue of A, then `lambda_(1)^(2), lambda_(2)^(2), ..., lambda_(n)^(2)` are eigenvalues of `A^(2)`.