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STD 12 - 3 and 4 . determinant and metrices — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 3 and 4 . determinant and metrices4 Marks
MCQ
If $A = \left[ {\begin{array}{*{20}{c}}3&4\\5&7\end{array}} \right]$, then $A\,(adj\,A)$=
  • A
    $2I$
  • B
    $|A|$
  • ✓
    $|A|I$
  • D
    None of these
✓

Answer

Correct option: C.
$|A|I$
c
(c) $A[adj(A)] = \left[ {\,\begin{array}{*{20}{c}}3&4\\5&7\end{array}\,} \right]\,\left[ {\,\begin{array}{*{20}{c}}7&{ - 4}\\{ - 5}&3\end{array}\,} \right] = \left[ {\,\begin{array}{*{20}{c}}1&0\\0&1\end{array}\,} \right] = |A|I$

$[\therefore |A| = 21-20=1]$

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