If A = [ * 20 c 1&2&3 - 2 &3& - 1 3&1&2 ]and I is a unit matrix o… - Vidyadip

MCQ

If $A = \left[ {\begin{array}{*{20}{c}}1&2&3\\{ - 2}&3&{ - 1}\\3&1&2\end{array}} \right]$and $I $is a unit matrix of ${3^{rd}}$order, then $({A^2} + 9I)$ equals

A
$2A$
B
$4A$
C
$6A$
✓
None of these

✓

Answer

Correct option: D.

None of these

d
(d) $A = \left[ {\begin{array}{*{20}{c}}1&2&3\\{ - 2}&3&{ - 1}\\3&1&2\end{array}} \right]$ ==> $A.A = {A^2} = \left[ {\begin{array}{*{20}{c}}6&{11}&7\\{ - 11}&4&{ - 11}\\7&{11}&{12}\end{array}} \right]\,,$

$I = \left[ {\begin{array}{*{20}{c}}1&0&0\\0&1&0\\0&0&1\end{array}} \right]$,then, ${A^2} + 9I = \,\left[ {\begin{array}{*{20}{c}}{15}&{11}&7\\{ - 11}&{13}&{ - 11}\\7&{11}&{21}\end{array}} \right]$.

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