Question

Assertion :If A = $\left(\begin{array}{cc}\cos \alpha & \sin \alpha \\ \cos \alpha & \sin \alpha \end{array}\right)$ and B = $\left(\begin{array}{cc}\cos \alpha & \cos \alpha \\ \sin \alpha & \sin \alpha \end{array}\right)$ then $AB\ne I$ Reason: The product of two matrices can never be equal to an identity matrix

• 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. Both Assertion and Reason are incorrect

Answer 1

The correct option is C Assertion is correct but Reason is incorrect

Reason is false

Assertion: Given $A=\left[\begin{array}{cc}\cos \alpha & \cos \alpha \\ \sin \alpha & \sin \alpha \end{array}\right]$ and $B=\left[\begin{array}{cc}\cos \alpha & \cos \alpha \\ \sin \alpha & \sin \alpha \end{array}\right]$
$AB=\left[\begin{array}{cc}\cos \alpha & \cos \alpha \\ \sin \alpha & \sin \alpha \end{array}\right]\times \left[\begin{array}{cc}\cos \alpha & \cos \alpha \\ \sin \alpha & \sin \alpha \end{array}\right]=\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right]\Rightarrow AB\ne 1$