Consider the endomorphism $f:E\to E$ and the basis $B_E$ and $B′_E$ along with the matrices $A=M(f,B_E,B′_E)$ and $P=M(B_E,B′_E)$
Calculate the following three matrices: $B=M(f,B′_E)$, $C=M(f,B′_E,B_E)$ and $D=M(f,B_E,B′_E)$
$\textbf{My answer:}$
$\hspace{0.5cm}\bullet B = M(f, B'_E)\longrightarrow B = P^{-1}\cdot A\cdot P$
$\hspace{0.5cm}\bullet C = M(f, B'_E, B_E)\longrightarrow C = P^{-1}\cdot A$
$\hspace{0.5cm}\bullet D = M(f, B_E, B'_E)\longrightarrow D = A$