A = [aij]ₘₓₙ is a square matrix if

The correct option is m = n.

In linear algebra, a matrix is represented by a rectangular array of numbers arranged in rows and columns. Let us denote the matrix as:
$$A={\left[a_{ij}\right]}_{m\times n}$$
Here, $m$ represents the total number of rows in the matrix, and $n$ represents the total number of columns.

By definition, a square matrix is a matrix that has the same number of rows as columns. This means the shape of the matrix forms a perfect square when laid out visually.

Therefore, for the matrix $A$ to be a square matrix, the number of rows ($m$) must be equal to the number of columns ($n$).

Thus, the mathematical condition for $A$ to be a square matrix is:
$$m=n$$