Let A and B be n × n matrices. Show that if AB is invertible, so is A. You cannot use Theorem 6(b), because you cannot assume that A and B are invertible. [Hint: There is a matrix W such that ABW = I. Why?]
Theorem 6(b):
If A and B are n × 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. That is, (AB)–1 = B–1A–1
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