Question

Assertion :The matrix $\left[\begin{array}{cccc}a& 0& 0& 0\\ 0& b& 0& 0\\ 0& 0& c& 0\end{array}\right]$ is a diagonal matrix Reason: $A\left[a_{ij}\right]$ is a square matrix such that $a_{ij}=0$ for all $i\ne j$, then $A$ is called diagonal 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. Assertion is incorrect but Reason is correct

Answer 1

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

Assertion: $A=\left[\begin{array}{cccc}a& 0& 0& 0\\ 0& b& 0& 0\\ 0& 0& c& 0\end{array}\right]$

It is not a diagonal matrix as a diagonal matrix is one that is a square matrix and all the elements $a_{ij}=0$ for all $i\ne j$

So Assertion is false. And the reason is a true definition of a diagonal matrix, so Reason is true.