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Easy

Question

If A and B are square matrices such that AB = B and BA = A, then A2 + B2 is equal to-

  1. 2AB    
  2. 2BA    
  3. A + B    
  4. AB    

The correct answer is: A + B



    We are given that  A and B are square matrices such that AB = B and BA = A and we are asked to find what  A2 + B2 is equal to
    A squared space plus space B squared space equals A A plus B B
equals A left parenthesis B A right parenthesis space plus space B left parenthesis A B right parenthesis
equals left parenthesis A B right parenthesis space A space plus space left parenthesis B A right parenthesis B
equals B A plus A B
equals A plus B

    Hence the correct answer is choice 3

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