Using the definition of the inverse of a matrix and the principles of matrix algebra, prove that if A and B are invertible matrices of the same order, then AB is invertible and = .
Definition: If we have a matrix, , such that for any matrix , then we call the identity matrix. It is a matrix of the same order of with a diagonal of 's on it's main diagonal and 0's everywhere else. Multiplying any matrix by the identity matrix gives the original matrix itself
in other words: