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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 $A = \left[ {\begin{array}{*{20}{c}}{ - 1}&0&0\\0&{ - 1}&0\\0&0&{ - 1}\end{array}} \right]$, then ${A^2}$is
  • A
    Null matrix
  • ✓
    Unit matrix
  • C
    $A$
  • D
    $2A$
✓

Answer

Correct option: B.
Unit matrix
b
(b) ${A^2} = \left[ {\begin{array}{*{20}{c}}{ - 1}&0&0\\0&{ - 1}&0\\0&0&{ - 1}\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}{ - 1}&0&0\\0&{ - 1}&0\\0&0&{ - 1}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}1&0&0\\0&1&0\\0&0&1\end{array}} \right] = I$.

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