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If A=diagonal...

Question

If $A = diagonal (3, 3, 3)$ , then $A^{4} =$

A

12 A

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B

81 A

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C

684 A

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D

27 A

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Solution

The correct option is D $27 A$
If $A = diag \cdot (a_{1}, a_{2} \dots, a_{n})$
then $A^{k} = diag \cdot (a_{1}^{k}, a_{2}^{k} \dots, a_{n}^{k}) A^{4} = diag \cdot (3^{4}, 3^{4}, 3^{4})$
$A^{4} = ⎡ ⎢ ⎣ \begin{matrix} 81 & 0 & 0 0 & 81 & 0 0 & 0 & 81 \end{matrix} ⎤ ⎥ ⎦ = 81 I = 27 A$

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