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Let G be the group of 2x2 invertible upper triangular matrices and H be the group of 2x2 invertible lower triangular matrices (both groups under multiplication). Are G and H isomorphic? Prove answer.

First I thought they were isomorphic, but couldn't find an isomorphism, so now I believe they are not isomorphic, but can't pinpoint exactly why.

Any suggestions?

First I thought they were isomorphic, but couldn't find an isomorphism, so now I believe they are not isomorphic, but can't pinpoint exactly why.

Any suggestions?

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