Q

# Solve it, - Matrices and Determinants - JEE Main-3

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

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N

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

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