Let A be an invertible matrix. Show that if λ is an eigenvalue of A, then 1/λ is an eigenvalue of A^−1. det((A-λI)) det((A-λI)^-1) =det(A^-1 - λ^-1 * I) =det(A-1-1/λ*I) Is this enough to show that? Another question I have is: Let A be an n × n matrix. Show that A is not invertible if and only if λ = 0 is an eigenvalue of A. Not sure how to approach this prob. det(A-λI)=0 det(A-0I)=0 det(A)=0 But idk how to show what the problem is asking.