Question

Assertion :$A=\left[\begin{array}{ccc}4& 0& 4\\ 2& 3& 2\\ 1& 2& 1\end{array}\right],B^{-1}=\left[\begin{array}{ccc}1& 3& 3\\ 1& 4& 3\\ 1& 3& 4\end{array}\right]$. Then $(AB{)}^{-1}$ does not exist. Reason: Since $|A|=0,(AB{)}^{-1}=B^{-1}{A}^{-1}$ is meaningless.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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

$\left|A\right|=4(3-4)+4(4-3)=0$

$\Rightarrow A^{-1}$ does not exist

$\Rightarrow {\left(AB\right)}^{-1}=B^{-1}{A}^{-1}$ does not exist

${\left(AB\right)}^{-1}$does not exist

Option A