Maths-
General
Easy

Question

If A and B are square matrices of size n × n such that A2 – B2 = (A – B) (A + B), then which of the following will be always true –

  1. AB = BA    
  2. either of A or B is a zero matrix    
  3. either of A or B is an identity matrix    
  4. A = B    

hintHint:

A squared minus B squared space equals left parenthesis A minus B right parenthesis left parenthesis A plus B right parenthesis
R. H. S. space equals left parenthesis A minus B right parenthesis left parenthesis A plus B right parenthesis equals A left parenthesis A plus B right parenthesis minus B left parenthesis A plus B right parenthesis
equals A squared plus A B minus B A minus B squared
T h i s space w i l l space b e c o m e space e q u a l space t o space L. H. S. space o n l y space w h e n space A B equals B A space

The correct answer is: AB = BA


    Given, that If A and B are square matrices of size n × n such that A2 – B2 = (A – B) (A + B), then which of the following will be always true

    Therefore, the correct option is AB=BA .

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