The adjugate method is a technique used to find the inverse of a square matrix. It involves calculating the adjugate, or adjoint, of the matrix, which is the transpose of its cofactor matrix. The inverse can then be obtained by dividing the adjugate by the determinant of the original matrix, provided the determinant is non-zero. This method is particularly useful for small matrices, such as 2x2 or 3x3 matrices. The adjugate method highlights the relationship between a matrix and its cofactors, making it a valuable tool in linear algebra and applications involving systems of equations and transformations.