Mathematics - Determinant Question with Solution | TestHub

Let $D=\left[\begin{array}{ll}a& b\\ c& d\\ e& f\end{array}\right]$ $\begin{array}{rl}& \therefore A+B-C=\left[\begin{array}{ll}1& 3\\ 3& 2\\ 2& 5\end{array}\right]+\left[\begin{array}{cc}-1& -2\\ 0& 5\\ 3& 1\end{array}\right]-\left[\begin{array}{ll}\mathrm{a}& \mathrm{b}\\ \mathrm{c}& \mathrm{d}\\ \mathrm{e}& \mathrm{f}\end{array}\right]\\ & \Rightarrow \left[\begin{array}{ll}1-1-\mathrm{a}& 3-2-\mathrm{b}\\ 3+0-\mathrm{c}& 2+5-\mathrm{d}\\ 2+3-\mathrm{e}& 5+1-\mathrm{f}\end{array}\right]=\left[\begin{array}{ll}0& 0\\ 0& 0\\ 0& 0\end{array}\right]\end{array}$ $\begin{array}{ll}-\mathrm{a}=0\Rightarrow \mathrm{a}=0,1-\mathrm{b}=0\Rightarrow \mathrm{b}=1,& \\ 3-\mathrm{c}=0\Rightarrow \mathrm{c}=3,& 7-\mathrm{d}=0\Rightarrow \mathrm{d}=7,\\ 5-\mathrm{e}=0\Rightarrow \mathrm{e}=5,& 6-\mathrm{f}=0\Rightarrow \mathrm{f}=6,\end{array}$ $\therefore D=\left[\begin{array}{ll}0& 1\\ 3& 7\\ 5& 6\end{array}\right]$