A is an invertible matrix, x is an eigenvector for A with an eiganvalue [tex]\lambda[/tex] [tex]\neq[/tex]0 Show that x is an eigenvector for A^-1 with eigenvalue [tex]\lambda[/tex]^-1
(A - I)x
The Attempt at a Solution
I know that I need to find x and then apply to the inverses of my Matrix and eigenvalue, but how do I know what matrix to use for A? Do I use the inverse matrix as it is an invertible matrix? Can I use any invertible matrix to prove this?
Thanks in advance.