Question

Assertion (A): Every scalar matrix is a diagonal matrix.
Reason (R): In a diagonal matrix, all the diagonal elements are 0.

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• B. Both Assertion (A) and Reason (R) are true, but Reason (R) is {not} the correct explanation of the Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Assertion (A) is false, but Reason (R) is true.

Hint:

A diagonal matrix has non-diagonal elements equal to 0, but its diagonal elements can be any value.

Answer 1

The Correct Option is C

A scalar matrix is a diagonal matrix with identical elements on the main diagonal. An illustration is:

\[ A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix} \]

This matrix is both a scalar matrix and a diagonal matrix. The statement "In a diagonal matrix, all the diagonal elements are 0" is false. Diagonal matrices can have any numerical value on their diagonal, not exclusively zero.

Final Answer: \( \boxed{[(C)] \text{Assertion (A) is true, but Reason (R) is false.}} \)