If A = [ * 20 c 2&0&0 0&2&0 0&0&2 ],then A^5 = - Vidyadip

MCQ

If $A = \left[ {\begin{array}{*{20}{c}}2&0&0\\0&2&0\\0&0&2\end{array}} \right],$then ${A^5} = $

A
$5A$
B
$10A$
✓
$16A$
D
$32A$

✓

Answer

Correct option: C.

$16A$

c
(c) $A = \left[ {\begin{array}{*{20}{c}}2&0&0\\0&2&0\\0&0&2\end{array}} \right]\, \Rightarrow {A^5} = \left[ {\begin{array}{*{20}{c}}{{2^5}}&0&0\\0&{{2^5}}&0\\0&0&{{2^5}}\end{array}} \right] = {2^4}\left[ {\begin{array}{*{20}{c}}2&0&0\\0&2&0\\0&0&2\end{array}} \right]$
$ = 16A$.

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