About Matrix Determinant

The determinant of a square matrix measures properties like area or volume scaling. For a 2x2 matrix \( A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \), it is:

• \( \det(A) = ad - bc \)

For a 3x3 matrix, it uses a more complex formula involving cofactors.

Example: \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), \( \det(A) = (1 \cdot 4) - (2 \cdot 3) = -2 \).