Mathematics - Matrix Question with Solution | TestHub

$A=\left[\begin{array}{ccc}1& -1& 1\\ 2& 1& -3\\ 1& 1& 1\end{array}\right]$ $\therefore |A|=\left[\begin{array}{ccc}1& -1& 1\\ 2& 1& -3\\ 1& 1& 1\end{array}\right]$ $=1(1+3)+1(2+3)+1(2-1)=4+5+1=10$ $\Rightarrow \mathrm{Adj}A={\left[\begin{array}{ccc}4& -5& 1\\ 2& 0& -2\\ 2& 5& 3\end{array}\right]}^T=\left[\begin{array}{ccc}4& 2& 2\\ -5& 0& 5\\ 1& -2& 3\end{array}\right]$ $\Rightarrow B=A^{-1}=\frac{1}{10}\left[\begin{array}{ccc}4& 2& 2\\ -5& 0& 5\\ 1& -2& 3\end{array}\right]\left[\because A^{-1}=\frac{1}{|A|}\mathrm{Adj}A\right]$ $\Rightarrow 10B=\left[\begin{array}{ccc}4& 2& 2\\ -5& 0& 5\\ 1& -2& 3\end{array}\right]$ Hence, $\alpha =5$