If A and B are square matrices of the same order, explain, why in… - Vidyadip

Question

If A and B are square matrices of the same order, explain, why in general:
(A + B)(A - B) ≠ A² - B².

✓

Answer

LHS = (A + B)(A - B)

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

= A² - AB + BA - B²

We know that a matrix does not have commutative property. So,

AB ≠ BA

Thus,

(A + B)(A - B) ≠ A² - B²

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