Originally Posted by

**BrownianMan** We are restricted in what we can use to write the proof for this question. Basically, all we can use is the Theorem that states:

**If A is an invertible matrix, then A^-1 is invertible and (A^-1)^-1 = A **

If A and B are n x n invertible matrices, then so is AB and the inverse of AB is the product of the inverses of A and B in the reverse order. (AB)^-1 = B^-1 A^-1

If A is an invertible matrix, then so is A^T , and the inverse of A^T is the transpose of A^-1 . That is (A^T)^-1 = (A^1)^T

The product of **n x n** invertible matrices is invertible, and the inverse is the product of their inverses in the reverse order.

We cannot use (ABC)D = I implies D(ABC) = I.

Also, another part to this question that I find confusing:

Let A, B, and C denote n x n matrices. Show that if A and AB are invertible, B is invertible. Same rules apply - we can only use the Theorem I posted.