Question:medium
If A and B are two square matrices of the same order, then (A + B)(A - B) is equal to:
If A and B are two square matrices of the same order, then (A + B)(A - B) is equal to:
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When expanding the product of two binomials involving matrices, always be mindful that matrix multiplication is not commutative, meaning \( AB \neq BA \).
Updated On: Mar 1, 2026
- \( A^2 - AB + BA - B^2 \)
- \( A^2 + AB - BA - B^2 \)
- \( A^2 - AB - BA - B^2 \)
- \( A^2 - B^2 + AB + BA \)
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The Correct Option is C
Solution and Explanation
The product of two binomials is given by: \[ (A + B)(A - B) = A^2 - AB + BA - B^2 \]. This identity is derived from the distributive property. However, because matrix multiplication is not commutative (i.e., \( AB eq BA \)), we cannot simplify \( -AB + BA \) to zero. Consequently, the accurate expansion is: \[ A^2 - AB - BA - B^2 \]
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