Question

If 'A' is square matrix, such that A² = A, then (7 + A)³ = 7A is equal to

विकल्प

• A

• 1 – A

• 1

• 3A

Answer 1

1

Explanation:

(I + A)³ – 7A = I³ + A³ + 3I²A + 3A²I – 7A

= 1 + A³ + 3A + 3A² – 7A

= 1 + A², A + 3A + 3A – 7A

= 1 + A, A – A

= 1 + A² – A

= 1 + A – A = 1

∴ (1 + A)³ – 7A = 1