The determinant of a square matrix is a scalar (a number) that indicates how that matrix behaves. It can be calculated from the numbers in the matrix.

The determinant of the matrix \displaystyle{ A } is written as \displaystyle{ \det(A) } or \displaystyle{ |A| } in a formula. Sometimes, instead of \displaystyle{ \det\left(\begin{bmatrix}a&b\\c&d\end{bmatrix}\right) } and \displaystyle{ \left|\begin{bmatrix}a&b\\c&d\end{bmatrix}\right| }, one simply writes \displaystyle{ \det\begin{bmatrix}a&b\\c&d\end{bmatrix} } and \displaystyle{ \left|\begin{matrix}a&b\\c&d\end{matrix}\right| }.