Definition:Matrix/Square Matrix

Definition
An $n \times n$ matrix is called a square matrix of order $n$.

That is, a square matrix is a matrix which has the same number of rows as it has columns

A square matrix $\left[{a}\right]_{n n}$ is usually denoted $\left[{a}\right]_{n}$.

In contrast, a non-square matrix can be referred to as a rectangular matrix.