# Thread: Eigenvalues and invertible matrices

1. ## Eigenvalues and invertible matrices

For which 2 x 2 matrices A does there exist an invertible matrix S such that AS = SD, where D = [2 0 ; 0 3]. Give your answer in terms of the eigenvalues of A.

Attempt at a solution: Do I find the inverse of D and then find the eigenvalues of D?

2. Originally Posted by noles2188
For which 2 x 2 matrices A does there exist an invertible matrix S such that AS = SD, where D = [2 0 ; 0 3]. Give your answer in terms of the eigenvalues of A.

Attempt at a solution: Do I find the inverse of D and then find the eigenvalues of D?

if you meant $D=\left(\begin{array}{cc}2&0\\0&3\end{array}\right )$ , then 2,3 are the eigenvalues of D since it is a diagonal matrix...

Tonio