The matrix $A= \begin{bmatrix}0&0&5\\0&5&0\\5&0&0\end{bmatrix}$ is a
(A) Diagonal matrix
(B) Scalar matrix
(C) Square matrix
(D) Symmetric matrix
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (C) and (D) only
The matrix is:
$A=\begin{pmatrix}0 & 0 & 5 \\ 0 & 5 & 0 \\ 5 & 0 & 0\end{pmatrix}$
Check properties:
• Not diagonal (non-zero off-diagonal elements). • Not scalar (not a multiple of identity). • It is square (3×3). • Also symmetric since $A = A^{T}$.
Correct answers: Square matrix and Symmetric matrix. (C) and (D)