# Definition:Matrix/Square Matrix

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## Definition

An $n \times n$ matrix is called a square matrix.

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.

### Order of Square Matrix

Let $\mathbf A$ be an $n \times n$ square matrix.

That is, let $\mathbf A$ have $n$ rows (and by definition $n$ columns).

Then the order of $\mathbf A$ is defined as being $n$.

## Examples

The $3 \times 3$ square matrix is as follows:

$\mathbf A = \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \\ \end{bmatrix}$