Determinant
The determinant is a special scalar value calculated from the elements of a square matrix. It provides important properties about the matrix, such as whether the matrix has an inverse and the scale factor for area or volume under the matrix transformation.
Example
For a $2 \times 2$ matrix $A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$, the determinant is calculated as $|A| = ad - bc$. If $A = \begin{pmatrix} 3 & 1 \\ 4 & 2 \end{pmatrix}$, then $|A| = (3 \times 2) - (1 \times 4) = 6 - 4 = 2$.