If , then is equal…

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

If A=[10121]A=\begin{bmatrix}1&0\\ \frac12&1\end{bmatrix}, then A100A^{100} is equal to (1) [10250]\begin{bmatrix}1&0\\25&0\end{bmatrix} (2) [10501]\begin{bmatrix}1&0\\50&1\end{bmatrix} (3) [10(12)1001]\begin{bmatrix}1&0\\\left(\frac12\right)^{100}&1\end{bmatrix} (4) None of these

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