Which amongst the following is true regarding matrices?

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

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

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(A + B)^{2} \neq A^{2} + 2 A B + B^{2}

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

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Solution

The correct option is B $(A + B)^{2} \neq A^{2} + 2 A B + B^{2}$
${(A + B)}^{2} = A^{2} + A B + B A + B^{2}$
${(A + B)}^{2} = A^{2} + 2 A B + B^{2}$ Only if $A B = B A$
$\Rightarrow {(A + B)}^{2} \neq A^{2} + 2 A B + B^{2}$ in all cases

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Similar questions

Which of the following is correct?
a) $(a - b)^{2} = a^{2} + 2 a b - b^{2}$
b) $(a - b)^{2} = a^{2} - 2 a b + b^{2}$
c) $(a - b)^{2} = a^{2} - b^{2}$
d) $(a + b)^{2} = a^{2} + 2 a b - b^{2}$

Q. Question 3

Which of the following is correct?
a)

(a - b)^{2} = a^{2} + 2 a b - b^{2}

(a - b)^{2} = a^{2} - 2 a b + b^{2}

(a - b)^{2} = a^{2} - b^{2}

(a + b)^{2} = a^{2} + 2 a b - b^{2}

Prove the following identities :

$(i) (a + b)^{2} = a^{2} + b^{2} + 2 a b$

$(i i) (a - b)^{2} = a^{2} + b^{2} - 2 a b$ [2 MARKS]

Q. Evaluate:

\sqrt{\frac{a^{2} + 2 a b + b^{2}}{a^{2} - 2 a b + b^{2}}}

Solve:

(a^{2} + b^{2} +2ab) - (a^{2} + b^{2} - 2ab)

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Which amongst the following is true regarding matrices?

The correct option is B (A+B)2≠A2+2AB+B2(A+B)2=A2+AB+BA+B2(A+B)2=A2+2AB+B2 Only if AB=BA⇒(A+B)2≠A2+2AB+B2 in all cases

The correct option is B $(A + B)^{2} \neq A^{2} + 2 A B + B^{2}$
${(A + B)}^{2} = A^{2} + A B + B A + B^{2}$
${(A + B)}^{2} = A^{2} + 2 A B + B^{2}$ Only if $A B = B A$
$\Rightarrow {(A + B)}^{2} \neq A^{2} + 2 A B + B^{2}$ in all cases