If A and B are any two matrices such tha

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Matrices

Question:

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

Options:

$B^2 A^3+A^3 B^2=0$

$A B+B A=0$

$B^3 A^4-A^4 B^3=0$

$A B(B-A)=0$

Correct Answer:

$B^3 A^4-A^4 B^3=0$

Explanation:

$(A-B)^2=A^2-A B-BA+B^2 = A^2 - 2AB + B^2$

⇒ AB = BA .....(1)

So $A^2B = ABA$

$A^2 B^2=B A A B$

$A^2 B^2=B A B A$

$A^2 B^2=B^2 A^2$

Similarly

$A^3 B^2=B^2 A^3$

$A^3 B^3=B^3 A^3$

$A^4 B^3=B^3 A^4$

⇒ $B^3 A^4-A^4 B^3=0$

Option C