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Algebra — MATHS STD 10 — Question

Tamilnadu BoardEnglish MediumSTD 10MATHSAlgebra5 Marks
Question
If $A=\left[\begin{array}{ll}2 & 5 \\ 4 & 3\end{array}\right], B=\left[\begin{array}{cc}1 & -3 \\ 2 & 5\end{array}\right]$ find $A B, B A$ and verify $A B=B A$ ?
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Answer

$\begin{aligned} & \text { Given } A=\left[\begin{array}{ll}2 & 5 \\ 4 & 3\end{array}\right], B =\left[\begin{array}{cc}1 & -3 \\ 2 & 5\end{array}\right] \\ & AB =\left[\begin{array}{ll}2 & 5 \\ 4 & 3\end{array}\right] \times\left[\begin{array}{cc}1 & -3 \\ 2 & 5\end{array}\right] \\ & =\left[\begin{array}{cc}2+10 & -6+25 \\ 4+6 & -12+15\end{array}\right] \\ & =\left[\begin{array}{cc}12 & 19 \\ 10 & 3\end{array}\right] \\ & BA =\left[\begin{array}{cc}1 & -3 \\ 2 & 5\end{array}\right] \times\left[\begin{array}{ll}2 & 5 \\ 4 & 3\end{array}\right] \\ & =\left[\begin{array}{cc}2-12 & 5-9 \\ 4+20 & 10+15\end{array}\right] \\ & =\left[\begin{array}{cc}-10 & -4 \\ 24 & 25\end{array}\right] \\ & AB \neq BA \end{aligned}$

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