if $T$ is isomorphism, how can I prove that $[T^{-1}]_B=[T]_B^{-1}$ for any base $B$ of $V$? given vector space $V$ so that $\dim(V)$ is finite , and linear-transformation $T:V \to V$. if $T$ is isomorphism, how can...--prophetes.ai

if $T$ is isomorphism, how can I prove that $[T^{-1}]_B=[T]_B^{-1}$ for any base $B$ of $V$? given vector space $V$ so that $\dim(V)$ is finite , and linear-transformation $T:V \to V$. if $T$ is isomorphism, how can I prove that $[T^{-1}]_B=[T]_B^{-1}$ for any base $B$ of $V$?

Using thae fact that$$[T]_B.[T^{-1}]_B=[T.T^{-1}]_B=\operatorname{Id}.$$