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Homework Statement
Let A be a square matrix.
If B is a square matrix satisfying AB=I
Homework Equations
Proof that B=A^-1
you can show this by showing that the inverse is unique.. ie. if AB=AC=I then B=C
I imagine that the point of this exercise is to show that the inverse is unique. You know that AB= I. Can you use that to prove that BA= I?
Suppose AC= CA= I. Can you prove that B= C (hint, if AB= I = AC, multiply on both sides, on the left, by C.)
Thanks.Actually, the problem is already solved for you. Just re-read the replies.
I'm sorry.I need to slove this problem without using the determinants.
My attempt at the solution is:_
First: If A is invertible:-
By multiplying by A^-1 on both sides on the left:_
(A^-1)(AB)=(A^-1)I
IB=A^-1
B=A^-1
Second: I need to show now, that A is invertible, to complete the solution.
This is the part which I'm confused about.