1. ## matrix proof 2

2. Originally Posted by nerdo

for part a, multiply the matrices then take the determinate. that is det(ab). then take det(a), det(b) separately and then find det(a)det(b) then show they are equal.

3. Originally Posted by GaloisTheory1
for part a, multiply the matrices then take the determinate. that is det(ab). then take det(a), det(b) separately and then find det(a)det(b) then show they are equal.

Oh i get it know, thanks for the help.

4. For the second part, take the determinant of both sides

$\displaystyle \det(ABA^{-1}B^{-1}) = \det(A)\det(B)\det(A^{-1})\det(B^{-1}) = \det(AA^{-1})\det(BB^{-1}) = 1$

$\displaystyle \det(2I_2) = 2$

Therefore no such matrices exist

5. Originally Posted by SimonM
For the second part, take the determinant of both sides

$\displaystyle \det(ABA^{-1}B^{-1}) = \det(A)\det(B)\det(A^{-1})\det(B^{-1}) = \det(AA^{-1})\det(BB^{-1}) = 1$

$\displaystyle \det(2I_2) = 2$

Therefore no such matrices exist
thanks i thought it was false, i was trying to figure it out for a while.