Question

If $A+B=\left[\begin{array}{cc}2& 3\\ 4& 5\end{array}\right]$ and $A=\left[\begin{array}{cc}1& 2\\ 0& 3\end{array}\right]$, then matrix $B$ is

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

Answer 1

The correct option is A $\left[\begin{array}{cc}1& 1\\ 4& 2\end{array}\right]$

As given $A+B=\left[\begin{array}{cc}2& 3\\ 4& 5\end{array}\right]$ and $A=\left[\begin{array}{cc}1& 2\\ 0& 3\end{array}\right]$

Substitute $A$ in $A+B$ we get,

$\left[\begin{array}{cc}1& 2\\ 0& 3\end{array}\right]+B=\left[\begin{array}{cc}2& 3\\ 4& 5\end{array}\right]$

$⟹$ $B=\left[\begin{array}{cc}2& 3\\ 4& 5\end{array}\right]-\left[\begin{array}{cc}1& 2\\ 0& 3\end{array}\right]$

$⟹$ $B=\left[\begin{array}{cc}(2-1)& (3-2)\\ (4-0)& (5-3)\end{array}\right]$

$\therefore$ $B=\left[\begin{array}{cc}1& 1\\ 4& 2\end{array}\right]$

Hence, option A is correct.