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Show that the abelian groups are isomorphic

buckylomax

New member
Aug 3, 2012
3
Hi there,

I'm trying to figure out this question:

Let A=[aij] be a 3x3 matrix with integer entries and let B=[bij] 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

MHB Oldtimer
Staff member
Feb 7, 2012
2,703
Can you be more precise about what you mean by "the Abelian groups represented by A and B"?