Question

Assertion :$\left[\begin{array}{ccc}3& 0& 0\\ 0& 4& 0\\ 0& 0& 7\end{array}\right]$ is a diagonal matrix. Reason: If $A=\left[a_{ij}\right]$ is a square matrix such that $a_{ij}=0,\forall i\ne j,$ then $A$ is called a 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. Both Assertion and Reason are incorrect

Answer 1

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

If $A={\left[a_{ij}\right]}_{n\times n}$ is a square matrix such that $a_{ij}=0$ for $i\ne j;$

then $A$ is called a diagonal matrix.

$\because a_{12}=a_{13}=a_{21}=a_{23}=a_{31}=a_{32}=0$

Thus, the given statement is true and $A=\left[\begin{array}{ccc}3& 0& 0\\ 0& 4& 0\\ 0& 0& 7\end{array}\right]$ is a diagonal matrix.