A matrix A = [aij]m×n is said to be symmetric if

The correct option is a_ij = a_ji.

Step-by-step Explanation:

A square matrix is defined as a symmetric matrix if it is equal to its own transpose. Let us denote the matrix as:
$$A=\left[a_{ij}\right]$$

The transpose of matrix $A$, denoted by $A^T$, is obtained by swapping its rows and columns. Therefore, the element in the $i$-th row and $j$-th column of $A^T$ is equal to the element in the $j$-th row and $i$-th column of $A$, which is $a_{ji}$.

For the matrix to be symmetric, we must have:
$$A=A^T$$

Comparing the corresponding elements of both matrices, this condition translates directly to:
$$a_{ij}=a_{ji}$$
for all indices $i$ and $j$. This means that the element located at row $i$, column $j$ must be identical to the element at row $j$, column $i$, representing symmetry across the main diagonal.