9reply ????
Let and B be different n x n matrices with real entries. I f A3=B3 and A2B=B2A , can 2+B2 be invertible?
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9 Answers
9consider
(A2 +B2)(A-B) = A3-B3-A2B+B2A = O
ie Δ(A2+B2) or Δ(A-B) is 0
when Δ(A2+B2) =0 , not invertible
9now if Δ(A-B) is 0 automatically Δ(A2+B2) is also 0
hence its never invertible
reason:
(A-B)2 = A2 + B2
9does that need a proof ?????
AB= -BA ie AB+BA=0
see carefully why do i need to prove
AB-BA=0
9o yeah b555 that was a typo thats not affecting the end result thanks edited
9but b555 in wat uve uploaded u cant just like that say A-B ≠O hence A2+B2 not invertible
what if Δ(A2+B2)≠0 u need to prove they r always 0
