Matrices

Concept:A symmetric matrix equals its transpose; for a square matrix, $a_{ij} = a_{ji}$ for all $i,j$.Explanation:The given matrix is $3 \times 3$.Compare entries: $a_{12} = 1$ and $a_{21} = 1$; $a_{13} = 2$ and $a_{31} = 2$; $a_{23} = -5$ and $a_{32} = -5$.All off-diagonal pairs are equal, so the matrix is symmetric.It is not a column matrix (needs single column), not a row matrix (needs single row), and not a null matrix (has non‑zero entries).Answer:Symmetric matrix