If A is a square matrix such that A2 = I, then (A – I)3 + (A + I)3

1.	If A is a square matrix such that A2 = I, then (A – I)3 + (A + I)3 – 7A is equal toA. AB. I – AC. I + AD. 3A
Answer» As, (A – I)³ + (A + I)³ Use a³ + b³ = (a + b)(a² + ab + b²) Also A² = I ∴ then (A – I)³ + (A + I)³ – 7A = 2A + 6A – 7A = A Clearly our answer matches with option (A) ∴ Option (A) is the correct answer.

If A is a square matrix such that A2 = I, then (A – I)3 + (A + I)3 – 7A is equal toA. AB. I – AC. I + AD. 3A

Answer»

As, (A – I)³ + (A + I)³

Use a³ + b³ = (a + b)(a² + ab + b²)

Also A² = I

∴ then (A – I)³ + (A + I)³ – 7A = 2A + 6A – 7A = A

Clearly our answer matches with option (A)

∴ Option (A) is the correct answer.

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If A is a square matrix such that A2 = I, then (A – I)3 + (A + I)3 – 7A is equal toA. AB. I – AC. I + AD. 3A

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