Question

If $A=\left[\begin{array}{cc}2& 3\\ 5& -2\end{array}\right]$, then $19A^{-1}$ is equal to

• A. $A^T$
• B. $2A$
• C. $\frac{1}{2}A$
• D. $A$

Answer 1

Answer: (A)

$A^T$

$A=\left[\begin{array}{cc}\begin{array}{c}2\\ 5\end{array}& \begin{array}{c}3\\ -2\end{array}\end{array}\right]adjA=\left[\begin{array}{cc}\begin{array}{c}-2\\ -3\end{array}& \begin{array}{c}-5\\ 2\end{array}\end{array}\right]\left|A\right|=-4-15=-19\therefore 19A^{-1}=-\left|\begin{array}{c}\begin{array}{cc}-2& -5\end{array}\\ \begin{array}{cc}-3& 2\end{array}\end{array}\right|=\left[\begin{array}{cc}\begin{array}{c}2\\ 3\end{array}& \begin{array}{c}5\\ -2\end{array}\end{array}\right]$