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
A has 3 rows and 3 columns. Comparing the entries on either side of the main diagonal:
\(a_{12} = a_{21} = 0\)
\(a_{13} = a_{31} = 5\)
\(a_{23} = a_{32} = 0\)
So A is a 3 × 3 matrix with \(A^T = A\), and its off-diagonal entry \(a_{13} = 5\) is not zero.
Checking the statements
(A) Diagonal matrix — Incorrect. The off-diagonal entry \(a_{13} = 5\) is not zero.
(B) Scalar matrix — Incorrect. A scalar matrix must be diagonal, and \(a_{13} = 5 \ne 0\).
(C) Square matrix — Correct. It has 3 rows and 3 columns.
(D) Symmetric matrix — Correct. \(a_{ij} = a_{ji}\) for all i, j, so \(A^T = A\).