Question

If $A=\left[\begin{array}{ccc}1& -3& 2\\ 2& 0& 2\end{array}\right]$ and $B=\left[\begin{array}{ccc}2& -1& -1\\ 1& 0& -1\end{array}\right]$, then the matrix $C$ such that $A+B+C$ is a zero matrix, is

• A. $\left[\begin{array}{ccc}-1& 4& -1\\ -1& 0& -1\end{array}\right]$
• B. $\left[\begin{array}{ccc}-3& 4& -1\\ -3& 0& -1\end{array}\right]$
• C. $\left[\begin{array}{ccc}-1& 1& -1\\ -1& 0& -1\end{array}\right]$
• D. $\left[\begin{array}{ccc}-1& 3& -1\\ -3& 0& -1\end{array}\right]$

Answer 1

The correct option is B $\left[\begin{array}{ccc}-3& 4& -1\\ -3& 0& -1\end{array}\right]$

$A+B+C=O$
$\Rightarrow C=-A-B$
$\Rightarrow C=-\left[\begin{array}{ccc}1& -3& 2\\ 2& 0& 2\end{array}\right]-\left[\begin{array}{ccc}2& -1& -1\\ 1& 0& -1\end{array}\right]$

$\Rightarrow C=\left[\begin{array}{ccc}-1-2& 3+1& -2+1\\ -2-1& 0-0& -2+1\end{array}\right]$

$\Rightarrow C=\left[\begin{array}{ccc}-3& 4& -1\\ -3& 0& -1\end{array}\right]$