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Q)

If $A$=$\begin{bmatrix} 2 & 1 \\3 & 4 \end{bmatrix}$, than (adj $A)A$=

\[\begin{array} {1 1}(1) \begin{bmatrix} \frac{1}{5}& 0 \\0 &\frac{1}{5} \end{bmatrix}& (2)\begin{bmatrix} 1 & 0 \\0 & 1 \end{bmatrix}\\ (3)\begin{bmatrix} 5 & 0 \\0 & -5 \end{bmatrix}& (4)\begin{bmatrix} 5 & 0 \\0 & 5 \end{bmatrix}\end{array}\]

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A)
$A$=$\begin{bmatrix} 2 & 1 \\3 & 4 \end{bmatrix}$
$(adj A) A = |A| I_2$
$|A|= \begin{vmatrix} 2 & 1 \\3 & 4 \end{vmatrix}$
$\qquad= 8-3=5 \neq 0$
$(adj \;A )A =5\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$
$=\begin{bmatrix} 5 & 0 \\0 & -5 \end{bmatrix}$
Hence 4 is the correct answer.
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