If A= 2 0 0 0 2 0 0 0 2 , then A^5 = - Vidyadip

MCQ

If $\text{A}=\begin{bmatrix} \text{2 0 0 0 2 0 0 0 2}\end{bmatrix},$ then $A^5 =$

A
$5A$
B
$10A$
✓
$16A$
D
$32A$

✓

Answer

Correct option: C.

$16A$

$\text{A}=\begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix}$
$\Rightarrow\text{A}=2\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$
$\Rightarrow\text{A}=2\text{I}$
$\Rightarrow\text{A}^5=(2\text{I})^5$
$\Rightarrow\text{A}^5=16\times2\text{I}$
$\Rightarrow\text{A}^5=16\begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix}$
$\Rightarrow\text{A}^5=16\text{A}$

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