I've been scouring the web and my textbook to no avail. I understand how to transform a matrix with respect to the standard basis, but not to a basis comprised of matrices.

I need to find the matrix of T with respect to a basis. My transformation matrix is:

$$ 
A =
\begin{bmatrix}
1 & 2 \\
0 & 3 \\ 
\end{bmatrix} $$

and I need to find it with respect to the basis:

$$
B = \left\{
\begin{bmatrix}
1& 0 \\
0 &0 \\ 
\end{bmatrix} ,
\begin{bmatrix}
0 & 1 \\
0 & 0 \\ 
\end{bmatrix},
\begin{bmatrix}
0 & 1 \\
0 & 1 \\ 
\end{bmatrix}\right\}
$$

I'm sorry my formatting is rough, the three B matrices are in the book as B = (Matrix 1, Matrix 2, Matrix 3).

I really don't understand this. My book has a column by column method that has completely stumped me.