Question

If $A+B=\left[\begin{array}{cc}10& 8\\ 8& 4\end{array}\right]$ and $A-B=\left[\begin{array}{cc}2& -4\\ 0& 6\end{array}\right],$ then $A$ is

• A. $\left[\begin{array}{cc}6& 2\\ 4& 5\end{array}\right]$
• B. $\left[\begin{array}{cc}6& 2\\ 4& 6\end{array}\right]$
• C. $\left[\begin{array}{cc}4& 6\\ 4& -1\end{array}\right]$
• D. $\left[\begin{array}{cc}1& 3\\ 4& 5\end{array}\right]$

Answer 1

Answer: (A)

We have,

$A+B=\left[\begin{array}{cc}10& 8\\ 8& 4\end{array}\right]andA-B=\left[\begin{array}{cc}2& -4\\ 0& 6\end{array}\right]$

Now, On adding them, we get

$A+B+A-B=\left[\begin{array}{cc}10& 8\\ 8& 4\end{array}\right]+\left[\begin{array}{cc}2& -4\\ 0& 6\end{array}\right]$

$\Rightarrow 2A=\left[\begin{array}{cc}12& 4\\ 8& 10\end{array}\right]$

$\Rightarrow A=\left[\begin{array}{cc}6& 2\\ 4& 5\end{array}\right]$

So, $\text{A}$ is the correct option.