Determine whether the given map [tex]\varphi[/tex] is an isomorphism of the first binary structure with the second.(adsbygoogle = window.adsbygoogle || []).push({});

< M_{2}(R), usual multiplication > with <R, usual multiplication> where [tex]\varphi[/tex](A) is the determinant of matrix A.

The determinant of the matrix is ad-bc, so [tex]\varphi[/tex](A)=ad-bc.

For this to be an isomorphism, I have to show that the function is one to one, onto and preserves the operations.

I'm having trouble getting this to work. Any suggestions?

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# Homework Help: Isomorphism: matrix determinant

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