One method is to apply row operations to reduce the matrix to the identity matrix, keeping track of the row operations, and then apply the same row operations to the identity matrix. The resulting matrix is the inverse. (If the matrix cannot be reduced to the identity matrix, there is no inverse.)

You can just use regular methods to compute the inverse of a square matrix, since the matrix representation of any invertible transformation is square, as for a linear transformation T: U→V to be invertible, it is required that dim(U)=dim(V).