Define eigenvalues and eigenvectors of a square matrix.

Let A be an invertible n n matrix, and let k ? R be a number. Prove that a vector v ? Rn is an eigenvector of A if and only if v is an eigenvector of (kIn + A?1).

Problem 10 . Define eigenvalues and eigenvectors of a square matrix . Let A be an invertible ~ x ~ matrix , and let KERR be a number . Prove that a vector V ER" is an eigenvector of A if and only if V is an eigenvector of ( kIn + A - 1 )