The matrix \(A=\begin{bmatrix}0 & 0 & 3\\ 0 & 3 & 0\\ 3 & 0 & 0\end{bmatrix}\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Square matrix
A has 3 rows and 3 columns, so it is a square matrix of order 3.
Its main diagonal (top left to bottom right) is 0, 3, 0, and the elements \(a_{13} = 3\) and \(a_{31} = 3\) off the diagonal are not zero.
Why the other options are incorrect
Option (1) diagonal matrix — Incorrect. A diagonal matrix has every off-diagonal element zero, but \(a_{13} = a_{31} = 3\). The 3s lie on the other diagonal, which does not count.
Option (3) Unit matrix — Incorrect. A unit matrix is diagonal with every diagonal element 1; A is not even diagonal.
Option (4) Scalar matrix — Incorrect. A scalar matrix is diagonal with equal diagonal elements; A’s diagonal is 0, 3, 0 and it has non-zero off-diagonal elements.