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3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
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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