1. Tardigrade
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  4. Let A=[a&0&0 0&a&0 0&0&a], then An is equal to

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Q. Let $A=\begin{bmatrix}a&0&0\\ 0&a&0\\ 0&0&a\end{bmatrix}, $ then $A^n$ is equal to

Matrices

Solution:

$A^{2}=\begin{bmatrix}a&0&0\\ 0&a&0\\ 0&0&a\end{bmatrix}\begin{bmatrix}a&0&0\\ 0&a&0\\ 0&0&a\end{bmatrix}=\begin{bmatrix}a^{2}&0&0\\ 0&a^{2}&0\\ 0&0&a^{2}\end{bmatrix}$
$A^{3}=\begin{bmatrix}a^{2}&0&0\\ 0&a^{2}&0\\ 0&0&a^{2}\end{bmatrix}\begin{bmatrix}a&0&0\\ 0&a&0\\ 0&0&a\end{bmatrix}=\begin{bmatrix}a^{3}&0&0\\ 0&a^{3}&0\\ 0&0&a^{3}\end{bmatrix}$