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If A and B are square matrices such that B = –A^–1BA, then

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If A and B are square matrices such that B = –A–1BA, then 

(a)   AB + BA = 0 

(b)   (A + B)2 = A2 + B2 

(c)   (A + B)2 = A2 + 2AB + B2 

(d)    (A + B)2 = A + B 

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1 Answer

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Best answer

Correct option  (a, b)

Explanation:

B = –A–1 BA ⇒ AB = –(AA–1) (BA)

⇒ AB = –IBA 

⇒ AB = –BA ⇒ AB + BA = 0

Now (A + B)2 = (A + B) (A + B) = A2 + AB + BA + B2 = A2 + B2

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