Let $\mathbf{A} = \begin{pmatrix} 15 & 25 \\ -9 & -15 \end{pmatrix}.$  Compute
\[\mathbf{I} + 2 \mathbf{A} + 3 \mathbf{A}^2 + 4 \mathbf{A}^3 + \dotsb.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $\mathbf{A} = \begin{pmatrix} 15 & 25 \\ -9 & -15 \end{pmatrix}.$  Compute
\[\mathbf{I} + 2 \mathbf{A} + 3 \mathbf{A}^2 + 4 \mathbf{A}^3 + \dotsb.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\begin{pmatrix} 31 & 50 \\ -18 & -29 \end{pmatrix}
Let $\mathbf{A} = \begin{pmatrix} 15 & 25 \\ -9 & -15 \end{pmatrix}.$  Compute
\[\mathbf{I} + 2 \mathbf{A} + 3 \mathbf{A}^2 + 4 \mathbf{A}^3 + \dotsb.\]
train