Question

If $A=\left[\begin{array}{cc}3& 2\\ 1& 4\end{array}\right]$, then $A(Adj.A)$ equals-

• 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 1

The correct option is A $\left[\begin{array}{cc}10& 0\\ 0& 10\end{array}\right]$

$A=\left[\begin{array}{cc}3& 2\\ 1& 4\end{array}\right]$

$adjA=\left[\begin{array}{cc}4& -2\\ -1& 3\end{array}\right]$

$A\left(adjA\right)=\left[\begin{array}{cc}3& 2\\ 1& 4\end{array}\right]\left[\begin{array}{cc}4& -2\\ -1& 3\end{array}\right]=\left[\begin{array}{cc}10& 0\\ 0& 10\end{array}\right]$