Let $ T:V\leftarrow V $ be a linear transformation. Let $B$ and $B_1$ be two bases of $V$.
Now consider the matrix of linear transformation $[M]_{B} ^B$ and $[M]_{B} ^{B_1}$. Does the characteristic polynomial of two matrices are same ?
Notation : $[M]_{B} ^{B_1}$ means Basis of domain is $B$ and Basis of co-domain is $B_1$
I tried to prove it but i didn't solve it. But both characteristic polynomial of both matrices should give same eigenvalue .