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(D) Given that $A$ and $B$ are square matrices of order $n 	imes n$. We know that the square of a matrix expression is defined as the product of the

Vedclass · Accepted Answer

${A^2} - AB - BA + {B^2}$

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(D) Given that $A$ and $B$ are square matrices of order $n 	imes n$. We know that the square of a matrix expression is defined as the product of the expression with itself. Therefore,${(A - B)^2} = (A - B)(A - B)$. Using the distributive property of matrix multiplication: $(A - B)(A - B) = A(A - B) - B(A - B)$ $= A^2 - AB - BA + B^2$. Since matrix multiplication is not commutative in general,$AB 
eq BA$,so we cannot simplify $-AB - BA$ to $-2AB$. Thus,the correct expression is $A^2 - AB - BA + B^2$.

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

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