a) If A and B are invertible matrices show that AB and BA are similar

b) Let A be an invertible matrix. Prove that if A is digonalizable, so is its inverse.(A^-1)

Thank You

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- Jan 22nd 2008, 10:19 PMsomestudent2Similarity and Digonalization in matrices
a) If A and B are invertible matrices show that AB and BA are similar

b) Let A be an invertible matrix. Prove that if A is digonalizable, so is its inverse.(A^-1)

Thank You - Jan 23rd 2008, 03:48 AMOpalg
- Jan 23rd 2008, 08:45 AMsomestudent2
Hi

for the second one by taking inverse on both sides we arive at

P^-1A^-1P = D^-1 ?

And this proves it (does it matter that Diagonal matrix is inversed now)? Or I need to make some additional calculations?

Thanks - Jan 23rd 2008, 11:10 AMOpalg