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Question: If A and B are square matrices of order n×n, then \((A - B)^{2}\)is equal to...

If A and B are square matrices of order n×n, then (A−B)2(A - B)^{2}is equal to

A

A2−B2A^{2} - B^{2}

B

A2−2AB+B2A^{2} - 2AB + B^{2}

C

A2+2AB+B2A^{2} + 2AB + B^{2}

D

A2−AB−BA+B2A^{2} - AB - BA + B^{2}

Answer

A2−AB−BA+B2A^{2} - AB - BA + B^{2}

Explanation

Solution

Given A and B are square matrices of order n×n we know that (A−B)2=(A−B)(A−B)=A2−AB−BA+B2(A - B)^{2} = (A - B)(A - B) = A^{2} - AB - BA + B^{2}