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If A and B are square matrices of size n x n such that A^{2}-B^{2}=(A-B)(A+B), then which of the following will be always true?

  • Option 1)

    A = B

  • Option 2)

    AB = BA

  • Option 3)

    either A or B is a zero matrix

  • Option 4)

    either A or B is an identity matrix

 

Answers (2)

As we learn tin 

Multiplication of matrices -

-

 

 A^{2}-B^{2}= (A-B)(A+B)

= AA+ AB- BA -BB

\therefore AB=BA

 


Option 1)

A = B

Incorrect option

Option 2)

AB = BA

Correct option

Option 3)

either A or B is a zero matrix

Incorrect option

Option 4)

either A or B is an identity matrix

Incorrect option

Posted by

Vakul

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