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Solving Inequalities

If A3 = 0 T...

Question

If $A^{3} = 0$ Then $1 + A + A^{2}$ equals :-

A

1 - A

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B

{(1 - A)}^{- 1}

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C

{(1 + A)}^{- 1}

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D

N.O.T.

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Solution

The correct option is B ${(1 - A)}^{- 1}$
$A^{3} = 0 ⟹ A^{3} - I = - I$
$(A - I) (I + A + A^{2}) = - I ⟹ I + A + A^{2} = (I - A)^{- 1}$

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Similar questions

A^{3} = 0

1 + A + A^{2}

{(a + \frac{1}{a})}^{2} = 3

a^{3} + \frac{1}{a^{3}}

a^{2} + \frac{1}{a^{2}} = 18

a \neq 0

a^{3} - \frac{1}{a^{3}}

{(a + \frac{1}{a})}^{2} = 3

a \neq 0

a^{3} + \frac{1}{a^{3}} = 0

a^{2} + \frac{1}{a^{2}} = 47

a \neq 0

a^{3} + \frac{1}{a^{3}}

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