# If A and B are square matrices of size n x n such that $\dpi{100} A^{2}-B^{2}=(A-B)(A+B),$ 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

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

N

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