MHB Show that the abelian groups are isomorphic

[buckylomax]

Hi there,

I'm trying to figure out this question:

Let A=[a_ij] be a 3x3 matrix with integer entries and let B=[b_ij] be it’s transpose. Let P and Q be the Abelian groups represented by A and B respectively. Show that P and Q are isomorphic by comparing the effects of row and column operations on A and B.

I've very stuck with this question. I figure I need to reduce both matrices to diagonal form and then compare them but I'm not sure how to get there. Any advices would be appreciated.

Thanks

B.

 

[Opalg]

Can you be more precise about what you mean by "the Abelian groups represented by A and B"?