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

Either of A or B is zero matrix

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A = B

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A B = B A

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Either of A or B is an identity matrix

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Solution

The correct option is C $A B = B A$
R.H.S. $= (A - B) (A + B) = A (A + B) - B (A + B)$
$= A^{2} + A B - B A - B^{2}$
This will become equal to L.H.S. only when $A B = B A$

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Similar questions

A

B

n \times n

A^{2} - B^{2} = (A - B) (A + B),

A

B

A^{2} = A, B^{2} = B, A B = B A = 0

A

A^{2} = A

A

B

A B = B A

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