## Nondefective Matrix

There is a problem in my book speaking of a nondefective matrix; however, my book neglects to define this term and the definitions I have found on the web aren't helping much.

Can someone help with this question?

Let A be a nondefective $nxn$ matrix with diagonalizing matrix X. Show that the matrix $Y=(X^{-1})^T$ diagonalizes to $A^T$.