If A is square matrix such that A 2 = A, then (I + A) � – 7 A is equal to

Question

Philoid · Accepted Answer

Given that A² = A

Calculating value of (I + A) � – 7 A:

⇒ I³ + A³ + 3I²A + 3IA² – 7A

⇒ I + A².A + 3A + 3A² – 7A (Iⁿ = I and I.A = A)

⇒ I + A.A + 3A + 3A – 7A (A² = A)

⇒ I + A² + 3A + 3A – 7A

⇒ I + A - A

⇒ I

Hence (I + A) � – 7 A = I.