Determinant and minors of lower-order matrices

To find the determinant of a 4 x 4 matrix, it's important to first understand what the determinant and minor of lower-order matrices are. The determinant function is recursive; to find the determinant of a 4 x 4 matrix, we need to find the determinants of several 3 x 3 and 2 x 2 matrices as well.

The determinant of a matrix is always a scalar value; only square matrices have a determinant. The determinant of a matrix remains the same if the matrix is transposed.

In the following sections, you will learn how to find the determinant of 2 x 2 matrices, the matrix of minors for any sized matrices, and the cofactor of any sized matrices. These methods are the building blocks of Laplace expansion, which you will use to find the determinant of any sized matrices.