If A is square matrix such that A2 = A,

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Determinants

Question:

If A is square matrix such that A² = A, then (I + A)³ - 8A is equal to :

Options:

I - A

Correct Answer:

I - A

Explanation:

A² = A

so (I + A)³ - 8A

(I + A)³ = (I + A)(I + A)(I + A)

= (I + A + A + A²)(I + A)(A² + 2A + I)(I + A)

= A³ + 2A² + A + A² + 2A + I

= A³ + 3A² + 3A + I

⇒ A³ + 3A² + 3A + I - 8A

= AA + 3A + 3A + I - 8A

A + 3A + 3A + I - 8A

⇒ I - A