When crammers rule is used in matrices?

Cramer's Rule is a mathematical theorem used to solve systems of linear equations with an equal number of equations and unknowns, provided the coefficient matrix is non-singular (i.e., has a non-zero determinant). It expresses the solution of the system in terms of determinants, where each variable is calculated as the ratio of two determinants: the determinant of the modified matrix (with one column replaced by the constants from the right-hand side) to the determinant of the coefficient matrix. While it can be efficient for small systems, it becomes computationally intensive for larger matrices due to the complexity of calculating determinants.