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Question

Assertion :The matrix ⎡⎢⎣100002000030⎤⎥⎦ is a diagonal matrix Reason: A=(aij)m×m is a square matrix such that entry aij=0∀i≠j, then A is called diagonal matrix.

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Solution

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

The given matrix having order 3×4

The given matrix having order 3×4

∴ Given matrix is not a square matrix.

Diagonal exist only in the square matrix

∴ 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.

∴ Assertion (A) is false but Reason (R) is true

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