(A) Given the equation: $(A + B)(A - B) = A^2 - B^2$Expanding the left side using the distributive property of matrix multiplication:$(A + B)(A - B) =

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(A) Given the equation: $(A + B)(A - B) = A^2 - B^2$Expanding the left side using the distributive property of matrix multiplication:$(A + B)(A - B) = A(A - B) + B(A - B)$$= A^2 - AB + BA - B^2$Equating this to the right side:$A^2 - AB + BA - B^2 = A^2 - B^2$Subtracting $A^2$ and adding $B^2$ to both sides:$-AB + BA = 0$Therefore:$BA = AB$

Class 12 Mathematics 3-4. Matrices and Determinants Types of matrices, Algebra of matrices

Medium

If $A$ and $B$ are two matrices and $(A + B)(A - B) = A^2 - B^2$,then

A
$AB = BA$
B
$A^2 + B^2 = A^2 - B^2$
C
$A'B' = AB$
D
None of these

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3-4. Matrices and Determinants

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Types of matrices, Algebra of matrices

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If $A$ and $B$ are two matrices and $(A + B)(A - B) = A^2 - B^2$,then

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