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Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices2 Marks
Question
If $\text{A}=\begin{bmatrix}1&-3&2\\2&0&2\end{bmatrix}$ and $\text{B}=\begin{bmatrix}2&-1&-1\\1&0&-1\end{bmatrix},$ find the matrix C such that A + B + C is zeor matrix.
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Answer

Given,
$\text{A}=\begin{bmatrix}1&-3&2\\2&0&2\end{bmatrix},\text{B}=\begin{bmatrix}2&-1&-1\\1&0&-1\end{bmatrix},$
And
$\text{A}+\text{B}+\text{C}=0$
$\Rightarrow\text{C}=-\text{A}-\text{B}+0$
$\Rightarrow\text{C}=-\text{A}-\text{B}$
$\Rightarrow\text{C}=-\begin{bmatrix}1&-3&2\\2&0&2\end{bmatrix}-\begin{bmatrix}2&-1&-1\\1&0&-1\end{bmatrix}$
$\Rightarrow\text{C}=\begin{bmatrix}-1&3&-2\\-2&0&-2\end{bmatrix}-\begin{bmatrix}2&-1&-1\\1&0&-1\end{bmatrix}$
$\Rightarrow\text{C}=\begin{bmatrix}-1-2&3+1&-2+1\\-2-1&0-0&-2+1\end{bmatrix}$
$\Rightarrow\text{C}=\begin{bmatrix}-3&4&-1\\-3&0&-1\end{bmatrix}$
Hence,
$\text{C}=\begin{bmatrix}-3&4&-1\\-3&0&-1\end{bmatrix}$

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