How can you determine if a matrix is singular or non-singular according to the chapter on matrix algebra?

To determine if a matrix is singular or non-singular, calculate its determinant. If the determinant is not equal to zero, the matrix is non-singular. If the determinant equals zero, the matrix is singular.

Every square matrix A has an associated determinant, denoted as |A|. A matrix is classified as non-singular if |A| ≠ 0, while it is singular if |A| = 0. This classification is fundamental in matrix algebra, as it indicates whether the matrix has an inverse or not.