# Thread: Invertible matrix question

1. ## Invertible matrix question

Let A 2 R^n x n and α belongs to R. Show that the matrix A-αI is invertible if, and only if, the matrix A^ T - αI is invertible, where I is the identity matrix.

Please help!!! have no idea to do this question.

2. Originally Posted by gklove56
Let A 2 R^n x n and α belongs to R. Show that the matrix A-αI is invertible if, and only if, the matrix A^ T - αI is invertible, where I is the identity matrix.

Please help!!! have no idea to do this question.
This would be clear if we knew these two matrices have the same eigenvalues. Do we? If so, how?