\begin{definition}[Definition:Determinant/Matrix/Order 2]
Let $\mathbf A = \sqbrk a_2$ be a square matrix of order $2$.
That is, let:
:$\mathbf A = \begin {bmatrix}
a_{1 1} & a_{1 2} \\
a_{2 1} & a_{2 2}
\end {bmatrix}$
Then the '''determinant''' of $\mathbf A$ is defined as:
{{begin-eqn}}
{{eqn | l = \begin {vmatrix} a_{1 1} & a_{1 2} \\ a_{2 1} & a_{2 2} \end{vmatrix}
      | r = \map \sgn {1, 2} a_{1 1} a_{2 2} + \map \sgn {2, 1} a_{1 2} a_{2 1}
      | c = 
}}
{{eqn | r = a_{1 1} a_{2 2} - a_{1 2} a_{2 1}
      | c = 
}}
{{end-eqn}}
where $\sgn$ denotes the sign of the permutation.
\end{definition}