square matrix

A square matrix has the same number of rows as columns.

Examples:

2. $\left(\begin{array}{c}\hfill 1\hfill \end{array}\right)$

The notation ${\mathrm{Mat}}_n(𝕂)$ is often used to signify the set of square matrices which are of order $n$ (size $n\times n$) with elements drawn from a field $𝕂$. Thus, one would use $a\in {\mathrm{Mat}}_3(ℂ)$ to declare that $a$ is a three-by-three matrix with elements that are complex numbers.

Property: Suppose $A$ and $B$ are matrices such that $AB$ is a square matrix. Then the product $BA$ is defined and also a square matrix.