If A is nonsingular, prove that the eigenvalues of `A^(-1)` are the reciprocals of the eigenvalue of A.

Explanation

Let a be an eigenvalue of A and X be a corresponding eigenvector. Then,
`AX=lambdaX`
or `X=A^(-1) (lambdaX)=lambda(A^(-1) X)`
or `1/lambda X=A^(-1) X" "[ :' " A is nonsingular" implies lambda ne 0]`
or `A^(-1) X=1/lambda X`
Therefore, `1//lambda` is an eigenvalue of `A^(-1)` and X is the corresponding eigenvector.