In the real vector space $\mathbb{R}^2$ consider the bases: $$B = (v_1, v_2) = ((1, 2), (1, 3))$$ $$B' = (v_1', v_2') = ((1, 0), (2, 1))$$
Let $f, g$ be endomorphisms on $\mathbb{R}^2$ having the matrices: $$[f]_B = \begin{pmatrix} 1 & 2\\ -1 & -1 \end{pmatrix}$$ $$[g]_{B'} = \begin{pmatrix} -7 & -13\\ 5 & 7 \end{pmatrix}$$
Determine $[f + g]_B$ and $[f \circ g]_{B'}$ using the change of bases matrices.
I found the change of bases matrices: $$T_{BB'} = \begin{pmatrix} -3 & -5\\ 2 & 3 \end{pmatrix}$$ $$T_{B'B} = \begin{pmatrix} 3 & 5\\ -2 & -3 \end{pmatrix}$$
Now, I used the known formula for finding $[g]_{B}$: $$[g]_B = T_{B'B}[g]_{B'}T_{BB'} = \begin{pmatrix} -20 & -32\\ 13 & 20 \end{pmatrix}$$
However, this result is wrong because it differs from the result I got by without using the change of basis matrix: $$\begin{pmatrix} -26 & -46\\ 19 & 33 \end{pmatrix}$$
Can you, please, help me figure out what I did wrong and how I should do it properly? Thank you in advance!