Find the B-matrix for the transformation $x \mapsto Ax$, where $B = \{b_1, b_2\}$.
$\begin{aligned} A = \begin{bmatrix} -3 & -1\\ 6 & -1 \end{bmatrix}, \quad b_1 = \begin{bmatrix} 1\\ 1 \end{bmatrix}, \quad b_2 = \begin{bmatrix} 1\\ 2 \end{bmatrix} \end{aligned}$
The B-matrix of the given transformation is $\begin{bmatrix} -4 & -5\\ 5 & 4 \end{bmatrix}$.
Try again.
If P is the matrix whose columns come from the vectors in B, then the B-matrix for the transformation $x \mapsto Ax$ is $[T]_B = P^{-1}AP.