Question

Assertion :The matrix $\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 2& 0& 0\\ 0& 0& 3& 0\end{array}\right]$ is a diagonal matrix Reason: $A=(a_{ij}{)}_{m\times m}$ is a square matrix such that entry $a_{ij}=0\forall i\ne j,$ then A is called diagonal matrix.

• A. Both (A) & (R) are individually true & (R) is correct explanation of (A)
• B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A)
• C. (A) is true but (R)is false
• D. (A) is false but (R ) is true

Answer 1

The correct option is D (A) is false but (R ) is true

The given matrix having order $3\times 4$

$\therefore$ Given matrix is not a square matrix.

Diagonal exist only in the square matrix

$\therefore$ Assertion (A) is false.

On the other side reason (R) satisfies the condition of diagonal matrix i.e. A diagonal matrix is the type of matrix which has non zero elements present in the diagonal. In other words, all other elements other than diagonal elements must be 0.

$\therefore$ Assertion (A) is false but Reason (R) is true