Some of the important properties of inverse matrices are:
The inverse of inverse matrix is equal to the original matrix.
If A and B are invertible matrices, then AB is also invertible. Thus, (AB)^-1 = B^-1A^-1
If A is nonsingular then (A^T)^-1 = (A^-1)^T
The product of a matrix and its inverse and vice versa is always equal to the identity matrix.