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Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices3 Marks
Question
If $A =\left[\begin{array}{cc}-1 & 3 \\ 2 & 4\end{array}\right], B =\left[\begin{array}{cc}2 & -3 \\ -4 & -6\end{array}\right]$ find the matrix $A B+B A$
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Answer

$\begin{aligned} & A=\left[\begin{array}{cc}-1 & 3 \\ 2 & 4\end{array}\right] \\ & B=\left[\begin{array}{cc}2 & -3 \\ -4 & -6\end{array}\right] \\ & AB =\left[\begin{array}{cc}-1 & 3 \\ 2 & 4\end{array}\right] \times\left[\begin{array}{cc}2 & -3 \\ -4 & -6\end{array}\right] \\ & =\left[\begin{array}{cc}-2-12 & 3-18 \\ 4-16 & -6-24\end{array}\right] \\ & =\left[\begin{array}{ll}-14 & -15 \\ -12 & -30\end{array}\right] \\ & BA =\left[\begin{array}{cc}2 & -3 \\ -4 & -6\end{array}\right] \times\left[\begin{array}{cc}-1 & 3 \\ 2 & 4\end{array}\right] \\ & =\left[\begin{array}{cc}-2-6 & 6-12 \\ 4-12 & -12-24\end{array}\right] \\ & =\left[\begin{array}{cc}-8 & -6 \\ -8 & -36\end{array}\right] \\ & \therefore A B+B A \\ & =\left[\begin{array}{ll}-14 & -15 \\ -12 & -30\end{array}\right]+\left[\begin{array}{cc}-8 & -6 \\ -8 & -36\end{array}\right] \\ & =\left[\begin{array}{cc}-14-8 & 15-6 \\ -12-8 & -30-36\end{array}\right] \\ & =\left[\begin{array}{ll}-22 & -21 \\ -20 & -66\end{array}\right] \text {. } \\ & \end{aligned}$

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