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STD 12 - 3 and 4 . determinant and metrices — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 3 and 4 . determinant and metrices1 Mark
MCQ
If $A = \left[ {\begin{array}{*{20}{c}}4&1\\3&2\end{array}} \right]$and $I = \left[ {\begin{array}{*{20}{c}}1&0\\0&1\end{array}} \right]$, ${A^2} - 6A = $
  • A
    $3I$
  • B
    $5I$
  • ✓
    $-5I$
  • D
    None of these
✓

Answer

Correct option: C.
$-5I$
c
(c) ${A^2} - 6\,A = \left[ {\begin{array}{*{20}{c}}4&1\\3&2\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}4&1\\3&2\end{array}} \right] - 6\left[ {\begin{array}{*{20}{c}}4&1\\3&2\end{array}} \right]$

$ = \left[ {\begin{array}{*{20}{c}}{19}&6\\{18}&7\end{array}} \right] - \left[ {\begin{array}{*{20}{c}}{24}&6\\{18}&{12}\end{array}} \right]$$\left[ {\begin{array}{*{20}{c}}{ - 5}&0\\0&{ - 5}\end{array}} \right] = - 5I$.

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