Let
\[\mathbf{A} = \begin{pmatrix} 4 & 1 \\ -9 & -2 \end{pmatrix}.\]Compute $\mathbf{A}^{100}.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let
\[\mathbf{A} = \begin{pmatrix} 4 & 1 \\ -9 & -2 \end{pmatrix}.\]Compute $\mathbf{A}^{100}.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\begin{pmatrix} 301 & 100 \\ -900 & -299 \end{pmatrix}
Let
\[\mathbf{A} = \begin{pmatrix} 4 & 1 \\ -9 & -2 \end{pmatrix}.\]Compute $\mathbf{A}^{100}.$
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