Determinants and Matrices — Maths STD 11 Science — Question

$=\left[\begin{array}{cc}4 & 2 \\ 10 & 7\end{array}\right]$

$\begin{aligned} \mathbf{B A} & =\left[\begin{array}{cc}0 & 4 \\ 2 & -1\end{array}\right]\left[\begin{array}{ll}1 & 2 \\ 3 & 5\end{array}\right] \\ & =\left[\begin{array}{cc}0+12 & 0+20 \\ 2-3 & 4-5\end{array}\right] \\ & =\left[\begin{array}{cc}12 & 20 \\ -1 & -1\end{array}\right] \neq \mathrm{AB}\end{aligned}$

Now $_r|A B|=\left|\begin{array}{cc}4 & 2 \\ 10 & 7\end{array}\right|=28-20=8$

$\begin{aligned} & |A|=\left|\begin{array}{cc}1 & 2 \\ 3 & 5\end{array}\right|=5-6=-1 \\ & |B|=\left|\begin{array}{cc}0 & 4 \\ 2 & -1\end{array}\right|=0-8=-8\end{aligned}$

∴ |A| . |B| = (-1).(-8) = 8 = |AB| ∴ AB ≠ BA, but |AB| = |A|.|B|