Question

Assertion :The matrix $A=\left(\begin{array}{ccc}-5& -8& 0\\ 3& 5& 0\\ 1& 2& -1\end{array}\right)$ is an involuntary matrix Reason: The matrix A satisfies the condition $A^2=I$

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

Answer 1

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

$A^2=A\times A=\left(\begin{array}{ccc}-5& -8& 0\\ 3& 5& 0\\ 1& 2& -1\end{array}\right)\times \left(\begin{array}{ccc}-5& -8& 0\\ 3& 5& 0\\ 1& 2& -1\end{array}\right)$

$=\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right)$

$\Rightarrow A^2=I$

$\therefore$ Assertion (A) and Reason (R) both are individually true and Reason (R) is correct explanation of Assertion (A).