# multiplication of matrices

• Jan 26th 2009, 04:25 AM
appleting
multiplication of matrices
Prove if there exists invertible 2x2 matrices A and B such that

A*B*A^-1*B^-1=2I

• Jan 26th 2009, 04:44 AM
GaloisTheory1
this question was recently posted...look in this category.
• Jan 26th 2009, 10:03 PM
Isomorphism
Quote:

Originally Posted by appleting
Prove if there exists invertible 2x2 matrices A and B such that

A*B*A^-1*B^-1=2I

If you are asking if there exist invertible matrices A and B such that $ABA^{-1}B^{-1} = 2I$, 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.