Question

If $A=\left[\begin{array}{cc}7& 2\\ 1& 3\end{array}\right]$ and $A+B=\left[\begin{array}{cc}-1& 0\\ 2& -4\end{array}\right],$ then matrix $B=$?

• A. $\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right]$
• B. $\left[\begin{array}{cc}6& 2\\ 3& -1\end{array}\right]$
• C. $\left[\begin{array}{cc}-8& -2\\ 1& -7\end{array}\right]$
• D. $\left[\begin{array}{cc}8& 2\\ -1& 7\end{array}\right]$

Answer 1

The correct option is C $\left[\begin{array}{cc}-8& -2\\ 1& -7\end{array}\right]$

$A+B=\left[\begin{array}{cc}-1& 0\\ 2& -4\end{array}\right]$

$A=\left[\begin{array}{cc}7& 2\\ 1& 3\end{array}\right]$

As we have learnt that we can subtract two matrices of the same order.

(Here, order of both the matrix is $2\times 2$)

So, we will subtract matrix $A$ from both sides of the equation.

We get,

$B=\left[\begin{array}{cc}-1& 0\\ 2& -4\end{array}\right]-\left[\begin{array}{cc}7& 2\\ 1& 3\end{array}\right]$

$B=\left[\begin{array}{cc}-1-7& 0-2\\ 2-1& -4-3\end{array}\right]$

(To subtract 2 matrices, we have to subtract their corresponding elements.)

$B=\left[\begin{array}{cc}-8& -2\\ 1& -7\end{array}\right]$

Hence, Option C is the correct answer