Similar Matrices

Definition

Let $A,B$ : Square matrices

If there exists invertible matrix $P$ such that $B=P^{-1}AP$

Then we say $B$ is similar to $A$

Note

Let $A,B$ : Square matrices. $\exists P,\det (P)\ne 0\ni B=P^{-1}AP⟹B\text{ similar to }A$