Question

The matrix $A = \begin{bmatrix} \sqrt{5} & 0 & 0 \\ 0 & \sqrt{2} & 0 \\ 0 & 0 & \sqrt{5} \end{bmatrix}$ is an:

• A. symmetric matrix
• B. identity matrix
• C. null matrix
• D. scalar matrix

Hint:

A scalar matrix is a special case of a diagonal matrix where all diagonal elements are the same.

Answer 1

The Correct Option is A

A scalar matrix is a diagonal matrix in which all the diagonal elements are equal. In this case, the matrix has the diagonal elements $\sqrt{5}$, $\sqrt{2}$, and $\sqrt{5}$, which are not equal. Therefore, this is not a scalar matrix. However, it is a diagonal matrix and the definition of a scalar matrix requires all diagonal elements to be the same. 
So, this is not a scalar matrix, making it a symmetric matrix as it satisfies $A = A^T$ for this case. The correct answer is (A).