Prove if there exists invertible 2x2 matrices A and B such that

A*B*A^-1*B^-1=2I₂

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- January 26th 2009, 04:25 AMappletingmultiplication of matrices
Prove if there exists invertible 2x2 matrices A and B such that

A*B*A^-1*B^-1=2I₂

- January 26th 2009, 04:44 AMGaloisTheory1
this question was recently posted...look in this category.

- January 26th 2009, 10:03 PMIsomorphism
If you are asking if there exist invertible matrices A and B such that , then we can easily say there does not. Use determinants.

However I think you dont know determinants and thats why they have given a 2x2 exercise. So it is the same as saying, AB = 2BA, Now write down the matrices 4 variables and equate the matrices term by term. This will show you that A or B cant be invertible.