Thread: AB = I_n can we obtain BA =I_n

Let A,B are square matrices n x n; and I_n is identity matrix.
If AB =I_n, can we obtain BA =I_n?
Thanks for your help.

Originally Posted by mahefo

Let A,B are square matrices n x n; and I_n is identity matrix.
If AB =I_n, can we obtain BA =I_n?
Thanks for your help.

Yes, since A and B are inverses of each other.

I know the definition of inverse matrix.
Can you show me the way from AB=I_n to get BA=I_n?
Thanks a lot.

Originally Posted by mahefo

I know the definition of inverse matrix.
Can you show me the way from AB=I_n to get BA=I_n?
Thanks a lot.

Ok, then you hopefully know that the product of two matrices is invertible iff every one of them is invertible, so in our case both matrices are invertible, but then:



Tonio

Originally Posted by tonio

well, that is not quite right because what we have is that has a right inverse. we don't know yet if the left inverse of exists or not.

Originally Posted by mahefo

Let A,B are square matrices n x n; and I_n is identity matrix.
If AB =I_n, can we obtain BA =I_n?
Thanks for your help.

see my second post in this thread: http://www.mathhelpforum.com/math-he...-fun-16-a.html