Two square matrices *A*,*B* of the same order *n* are **similar** if there exists an invertible matrix *P* of order
*n* such that
*B*= *P*^{-1}*AP*.

- 1.
- The identity matrix
*I*is similar only to itself. - 2.
- The matrices and are similar. (Check it with ).

- 1.
- If
*A*and*B*are similar, then |*A*|=|*B*|. - 2.
- If
*A*and*B*are similar, then . - 3.
- Similar matrices have the same characteristic polynomial, thus the same eigenvalues (with the same multiplicities).