If A = [ * 20 c 3&4 5&7 ], then A ,(adj ,A)=

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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