If A is idempotent matrix and A+B = I, then B is

nilpotent matrix

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idempotent mattrix

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involutary matrix

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orthogonal matrix

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Solution

The correct option is B idempotent mattrix
$∵ A$ is idempotent

$∴ A^{2} = A$

Now,
$B = I - A$

$B^{2} = (I - A)^{2}$

$B^{2} = (I + A^{2} - 2 A)$

$B^{2} = (I + A - 2 A)$

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

Therefore, B is Idempotent

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Similar questions

A = I - B

A = I - B

A

A^{2} = A

B = I - A

If A is an idempotent matrix and A + B =I, then which of the following is true?

A

(2 I + A)^{4} = a I + b A, (I is unit matrix), a, b \in R .

(a + b) =

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