it is possible to find another way to solve the system of equations when the determinant is zero without using the inverse of the matrix directly.
Why can’t we find the inverse of a matrix when the determinant is equal to zero?
Let’s remind that the determinant of a matrix is a numeric value that can be calculated from the elements of the matrix. The determinant of a matrix is used in different areas of mathematics and physics to solve problems involving matrices. Its relevance with the inverse of a matrix depends on the following equivalence, where the inverse of a matrix only exists if the determinant is different from zero, as it means division by zero: