CBSE 2025, Set 2

Question

**Assertion (A):** $A=	ext{diag} [3, 5, 2]$ is a scalar matrix of order $3	imes3$.
**Reason (R):** If a diagonal matrix has all non-zero elements equal, it is known as a scalar matrix. 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.

Edvaya · Accepted Answer

The correct answer is Assertion (A) is false, but Reason (R) is true.. **Solution:**

**Assertion (A):** A scalar matrix is a specific type of diagonal matrix where all the diagonal elements are identical. The given matrix is a diagonal matrix with elements $3, 5,$ and $2$. Since these elements are not equal, $A$ is just a regular diagonal matrix, not a scalar matrix. Thus, Assertion (A) is **false**.

**Reason (R):** The mathematical definition states that a diagonal matrix whose principal diagonal elements are all equal is called a scalar matrix. This statement is definitionally **true**.

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

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