If A= [ ll 3 & 2 1 & 4 ], then A(adj A)= - Vidyadip

MCQ

If $A=\left[\begin{array}{ll}3 & 2 \\ 1 & 4\end{array}\right]$, then $A(\operatorname{adj} A)=$

✓
$\left[\begin{array}{cc}10 & 0 \\ 0 & 10\end{array}\right]$
B
$\left[\begin{array}{cc}0 & 10 \\ 10 & 0\end{array}\right]$
C
$\left[\begin{array}{cc}10 & 1 \\ 1 & 10\end{array}\right]$
D
None of these

✓

Answer

Correct option: A.

$\left[\begin{array}{cc}10 & 0 \\ 0 & 10\end{array}\right]$

(A) Using Shortcut 4(i),
$A (\operatorname{adj} A )=| A | \cdot I _{ n }$
$\therefore \quad A (\operatorname{adj} A )=\left|\begin{array}{ll}3 & 2 \\ 1 & 4\end{array}\right|\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]=\left[\begin{array}{cc}10 & 0 \\ 0 & 10\end{array}\right]$

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