Answer
True
Work Step by Step
A matrix representation of $T$ relative to the bases $B$ and $C$ is given by $[T]_B^C$ , then $B$ shows a basis for $V$ and $C$ shows a basis for $W$.
and bases $B_1=C_1=\{(1,0), (0,1) \} $; $B_2=\{(1,0), (0,1) \} $ and $C_2=\{(1,0), (0,1) \} $
This implies that $[T_1]_{B_{1}}^{C_{1}}=[T_2]_{B_{2}}^{C_{2}}=\begin{bmatrix}1&0\\0&1\end{bmatrix}$
Therefore, the given statement is True.
