If A = [ ll 3 & 2 1 & 4 ], then write the value of A .(adj A ). - Vidyadip

Question

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

✓

Answer

$A_{11}=4, A_{12}=-1, A_{21}=-2, A_{22}=3$$
\begin{aligned}
\operatorname{adj} A & =\left[\begin{array}{cc}
4 & -1 \\
-2 & 3
\end{array}\right]^{\prime}=\left[\begin{array}{cc}
4 & -2 \\
-1 & 3
\end{array}\right] \\
\text { A. }(\operatorname{adj} A) & =\left[\begin{array}{ll}
3 & 2 \\
1 & 4
\end{array}\right]\left[\begin{array}{cc}
4 & -2 \\
-1 & 3
\end{array}\right] \\
& =\left[\begin{array}{cc}
10 & 0 \\
0 & 10
\end{array}\right] \text {}
\end{aligned}
$

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