DeterminantHard
Question
If A and B are two matrices such that AB = B and BA = A, then A2 + B2 =
Options
A.2AB
B.2BA
C.A + B
D.AB
Solution
AB = B
Premultiply both sides by B
BAB = B2
⇒ AB = B2 ⇒ B = B2
Similarly
BA = A ⇒ ABA = A2 ⇒ BA = A2
⇒ A = A2
Premultiply both sides by B
BAB = B2
⇒ AB = B2 ⇒ B = B2
Similarly
BA = A ⇒ ABA = A2 ⇒ BA = A2
⇒ A = A2
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