If A and B are two square matrices of the same order, then (A + B)(A - B) is equal to:
Show Hint
- \( A^2 - AB + BA - B^2 \)
- \( A^2 + AB - BA - B^2 \)
- \( A^2 - AB - BA - B^2 \)
- \( A^2 - B^2 + AB + BA \)
The Correct Option is C
Solution and Explanation
We can use the formula for the product of two binomials: \[ (A + B)(A - B) = A^2 - AB + BA - B^2 \] This result follows from the distributive property.
Now, since matrix multiplication is not commutative, we cannot assume \( AB = BA \).
Therefore, the correct expression is: \[ A^2 - AB - BA - B^2 \]
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