Question

If A and B are both square n x n matrices,

If AB = I,
prove BA = I

Presumably you have to do this without using the usual properties of the inverse of matrices. But we do need to use that if there exists a matrix B such that

A B = I

then the equation A X = 0 has the unique solution:

X = 0

So, let's start with:
AB = I

Multiply both sides by A on the right:

(AB)A = A

Now you use that (AB)A = A(BA) and you can rewrite the above equation as:

A(BA - I) = 0

And it follows that

BA = I

well if u decmial the 7 to a 6 good luck with that ..........