Definition:Determinant/Matrix/Order 2

Definition
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:

where $\sgn$ denotes the sign of the permutation.