Question

The matrix $A = \begin{pmatrix} \sqrt{3} & 0 & 0 \\ 0 & \sqrt{2} & 0 \\ 0 & 0 & \sqrt{5} \end{pmatrix}$ is a/an :

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

Hint:

A symmetric matrix satisfies $A = A^T$, which is true for diagonal matrices as well.

Answer 1

The Correct Option is D

A symmetric matrix is a square matrix that is equal to its transpose. The given matrix has diagonal elements, and the off-diagonal elements are zero. The matrix is a diagonal matrix, and diagonal matrices are always symmetric because they are equal to their own transposes.
Hence, the correct classification is a symmetric matrix.