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# If $A$=$\begin{bmatrix} 0 & 0 \\0 & 5 \end{bmatrix}$, then $A^{12}$ is

$\begin{array} {1 1}(1)\begin{bmatrix} 0 & 0 \\0 & 60 \end{bmatrix}&(2)\begin{bmatrix} 0 & 0 \\0 & 5^{12} \end{bmatrix}\\(3)\begin{bmatrix} 0 & 0 \\0 & 0 \end{bmatrix}&(4)\begin{bmatrix} 1 & 0 \\0 & 1\end{bmatrix}\end{array}$

Can you answer this question?

$A=\begin{bmatrix} 1 & 0 \\0 & 5\end{bmatrix}$
$A^2=\begin{bmatrix} 0 & 0 \\0 & 5\end{bmatrix} \begin{bmatrix} 0 & 0 \\0 & 5\end{bmatrix}$
$\qquad=\begin{bmatrix} 0 & 0 \\0 & 25\end{bmatrix}$
$\qquad=\begin{bmatrix} 0 & 0 \\0 & 5^2 \end{bmatrix}$
$A^{12}=\begin{bmatrix} 1 & 0 \\0 & 5^{12}\end{bmatrix}$
Hence 2 is the correct answer.
answered May 5, 2014 by