Question

If $A=\left[\begin{array}{cc}-3& -5\\ -6& 0\end{array}\right]$ and $A+B=2I$. Find $B$.

• A. $\left[\begin{array}{cc}1& 2\\ -3& -6\end{array}\right]$
• B. $\left[\begin{array}{cc}3& 5\\ 3& 6\end{array}\right]$
• C. $\left[\begin{array}{cc}5& 5\\ 6& 2\end{array}\right]$
• D. $\left[\begin{array}{cc}1& 2\\ 3& 2\end{array}\right]$

Answer 1

The correct option is C $\left[\begin{array}{cc}5& 5\\ 6& 2\end{array}\right]$

Given, $A=\left[\begin{array}{cc}-3& -5\\ -6& 0\end{array}\right]$ and $A+B=2I[\because \left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]]$

$\Rightarrow \left[\begin{array}{cc}-3& -5\\ -6& 0\end{array}\right]+B=\left[\begin{array}{cc}2& 0\\ 0& 2\end{array}\right]$

$\Rightarrow B=\left[\begin{array}{cc}2& 0\\ 0& 2\end{array}\right]-\left[\begin{array}{cc}-3& -5\\ -6& 0\end{array}\right]$

$\Rightarrow B=\left[\begin{array}{cc}5& 5\\ 6& 2\end{array}\right]$

$\therefore$Option C will be correct.