Question

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

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

Answer 1

Answer: (A)

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

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

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

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

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

$\therefore$ Option A will be correct.