Question

If $|A|=3$ and $A^{-1}=\left[\begin{array}{cc}3& -1\\ -5/3& 3\end{array}\right]$ write $adjA$

Answer 1

$\left|A\right|=3,A^{-1}=\left[\begin{array}{cc}3& -1\\ \frac{-5}{3}& 3\end{array}\right]$

we know that $A^{-1}=\frac{adjA}{\left|A\right|}$

$\therefore adjA=A^{-1}\times \left|A\right|=\left[\begin{array}{cc}3& -1\\ \frac{-5}{3}& 3\end{array}\right]\times 3=\left[\begin{array}{cc}9& -3\\ -5& 9\end{array}\right]$