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Algebra — MATHS STD 10 — Question

Tamilnadu BoardEnglish MediumSTD 10MATHSAlgebra5 Marks
Question
If $A=\left[\begin{array}{cc}1 & 9 \\ 3 & 4 \\ 8 & -3\end{array}\right], B=\left[\begin{array}{ll}5 & 7 \\ 3 & 3 \\ 1 & 0\end{array}\right]$ then verify that $A+(-A)=(-A)+A=0$
✓

Answer

$\begin{aligned} & A+(-A)=\left[\begin{array}{cc}1 & 9 \\ 3 & 4 \\ 8 & -3\end{array}\right]+(-)\left[\begin{array}{cc}1 & 9 \\ 3 & 4 \\ 8 & -3\end{array}\right] \\ & =\left[\begin{array}{cc}1 & 9 \\ 3 & 4 \\ 8 & -3\end{array}\right]+\left[\begin{array}{cc}-1 & -9 \\ -3 & -4 \\ -8 & 3\end{array}\right] \\ & =\left[\begin{array}{ll}0 & 0 \\ 0 & 0 \\ 0 & 0\end{array}\right] \\ & =0 \\ & (-A)+A=-\left[\begin{array}{cc}1 & 9 \\ 3 & 4 \\ 8 & -3\end{array}\right]+\left[\begin{array}{cc}1 & 9 \\ 3 & 4 \\ 8 & -3\end{array}\right] \\ & =\left[\begin{array}{cc}-1 & -9 \\ -3 & -4 \\ -8 & 3\end{array}\right]+\left[\begin{array}{cc}1 & 9 \\ 3 & 4 \\ 8 & -3\end{array}\right] \\ & =\left[\begin{array}{ll}0 & 0 \\ 0 & 0 \\ 0 & 0\end{array}\right] \\ & \end{aligned}$
= 0 ....(2)
From (1) and (2) we get
A + (– A) = (– A) + A = 0

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