Question

$A$: If $A=\left\{\begin{array}{cc}1& -1\\ -1& 1\end{array}\right\}$ and $B=\left\{\begin{array}{cc}2& 2\\ 2& 2\end{array}\right\},$ then $AB=0$
$R$: If $AB=0\Rightarrow A$ or $B$ need not be null matrices.

The correct answer is

• A. Both $A$ and $R$ are true, $R$ is correct explanation to $A$
• B. Both $A$ and $R$ are true but $R$ is not correct explanation to $A$
• C. $A$ is true, $R$ is false
• D. $A$ is false, $R$ is true

Answer 1

The correct option is A Both $A$ and $R$ are true, $R$ is correct explanation to $A$

If $A=\left\{\begin{array}{cc}1& -1\\ -1& 1\end{array}\right\};B=\left\{\begin{array}{cc}2& 2\\ 2& 2\end{array}\right\}$
Then, $AB=\left\{\begin{array}{cc}1\times 2-1\times 2& 1\times 2-1\times 2\\ -1\times 2+1\times 2& -1\times 2+1\times 2\end{array}\right\}=O$
Hence both statement are correct and Reason is correct explanation of Assertion.