Question

Assertion (A): A = diag [3 5 2] is a scalar matrix of order 3 × 3.

Reason (R): If a diagonal matrix has all non-zero elements equal, it is known as a scalar matrix.

Options

• Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A).

• Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

• Assertion (A) is true but Reason (R) is false.

• Assertion (A) is false but Reason (R) is true.

Answer 1

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

Explanation:

A = diag [3 5 2] 

= `[(3, 0, 0), (0, 5, 0), (0, 0, 2)]`

Since the diagonal elements are not all equal, the given matrix cannot be a scalar matrix.

Therefore, the assertion is false.

A diagonal matrix in which all the diagonal entries are equal is called a scalar matrix.

Hence, the reason is true.