# 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 is usually denoted $\sqbrk a_n$ in preference to $\sqbrk a_{n n}$.

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

### Real $2 \times 2$ Square Matrix

A $2 \times 2$ real square matrix is an array of $4$ real numbers $p, q, r, s$ arranged as:

$\mathbf A = \begin{bmatrix} p & q \\ r & s \end{bmatrix}$

### $3 \times 3$ Square Matrix

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

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

## Also see

• Results about square matrices can be found here.