The matrix \( \begin{bmatrix}0 & 0 & 1\\0 & 1 & 0\\1 & 0 & 0\end{bmatrix} \) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → a symmetric matrix
Comparing each entry \( a_{ij} \) with \( a_{ji} \):
\( \displaystyle a_{12}=a_{21}=0 \)
\( \displaystyle a_{13}=a_{31}=1 \)
\( \displaystyle a_{23}=a_{32}=0 \)
So \( A^T=A \) and the matrix is symmetric.
Why the other options are incorrect
Option (1) an identity matrix — Incorrect. The identity matrix has 1s on the leading diagonal, but here \( a_{11}=a_{33}=0 \); the 1s lie on the other diagonal.
Option (2) a diagonal matrix — Incorrect. A diagonal matrix has all off-diagonal entries 0, but here \( a_{13}=a_{31}=1 \).
Option (3) a scalar matrix — Incorrect. A scalar matrix is a diagonal matrix with equal diagonal entries; this matrix is not even diagonal.