If A And B Are Square Matrices of the Same Order, Explain, Why in General (A − B)2 ≠ A2 − 2ab + B2 - Mathematics

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If A and B are square matrices of the same order, explain, why in general

(A − B)² ≠ A² − 2AB + B²

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उत्तर

$(i i) L H S = {(A - B)}^{2}$

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

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

$= A^{2} - A B - B A + B^{2}$

We know that a matrix does not have commutative property. So,
AB ≠ BA
Thus,

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Algebraic Operations on Matrices - Multiplication of Matrices

या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

Q 67.2 Q 67.1 Q 67.3

पाठ 5: Algebra of Matrices - Exercise 5.3 [पृष्ठ ४६]

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पाठ 5 Algebra of Matrices
Exercise 5.3 | Q 67.2 | पृष्ठ ४६

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If A And B Are Square Matrices of the Same Order, Explain, Why in General (A − B)2 ≠ A2 − 2ab + B2 - Mathematics

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If A And B Are Square Matrices of the Same Order, Explain, Why in General (A − B)2 ≠ A2 − 2ab + B2 - Mathematics

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