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Multiplication of Matrices

For two matri...

Question

$For two matrices A and B which are multiplication compatible, (A + B)^{2} = A^{2} + 2 AB + B^{2}$

A

False

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B

True

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Solution

The correct option is A False

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Similar questions

Q. If A and B are square matrices of the same order, explain, why in general
(i) (A + B)² ≠ A² + 2AB + B²
(ii) (A − B)² ≠ A² − 2AB + B²
(iii) (A + B) (A − B) ≠ A² − B².

Q. If A and B are two square matrices such that

B = - A^{- 1} B A

(A + B)^{2}

Q. If A and B are matrices of the same order, then

{(A + B)}^{2} = A^{2} + 2 A B + B^{2}

is possible, iff

Show that if A and B are square matrices such that AB = BA, then $(A + B)^{2} = A^{2} + 2 A B + B^{2}$ .

Q. If A and B are square matrices of the same order such that AB = BA, then show that (A + B)² = A² + 2AB + B².

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