The term "adjugate" refers to a matrix derived from another matrix, specifically the cofactor matrix. It is formed by taking the cofactor of each element in the original matrix and then transposing the resulting matrix. The adjugate is useful in various mathematical applications, particularly in finding the inverse of a matrix. In the context of linear algebra, the adjugate plays a crucial role in calculating the inverse of a square matrix. If a matrix is invertible, the inverse can be expressed as the adjugate divided by the determinant of the original matrix. This relationship highlights the importance of the adjugate in solving systems of equations and other mathematical problems.