If A and B are square matrices of the sa

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Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Algebra

Question:

If A and B are square matrices of the same order, then the value of $(A+B)(A-B)$ is equal to:

Options:

$A^2-B^2$

$A^2-B A-A B-B^2$

$A^2-B^2+B A-A B$

$A^2-B A+B^2+A B$

Correct Answer:

$A^2-B^2+B A-A B$

Explanation:

The correct answer is Option (3) → $A^2-B^2+B A-A B$

$(A+B)(A-B)=A(A-B)+B(A-B)$

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

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

The value is $A^2 - B^2 + BA - AB$.