ac.commutative algebra - Filtration over tensor product

gr.group idea – If $ ABCD = DCBA = I $, does it denote $A = C$ and $B = D$? retort

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gr.group idea – If $ ABCD = DCBA = I $, does it denote $A = C$ and $B = D$?

If $A,B,C,D$ are invertible sq. matrices of precise numbers and $ ABCD = DCBA = I $, the place $I$ is an identification matrix,
does it denote $A = C$ and $B = D$?

I went so far as writing $ ABCD = CDAB = DCBA = BADC = CBAD = ADCB = BCDA = DABC = I $.

I’m not a mathematician, however I maintain a emotion this could breathe resolved utilizing group algebra and extra superior theories.

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