Question

if a is a square matrix such that a² = a, then write the value of 7a - (i + a)³ where i is an identity matrix.​​

Answer 1

Answer:

given A2=A

7A−(I+A)3=7A−[I3+3A2I+3AI2+A3]

=7A−[I+3A+3A+A2.A]

=7A−[I+3A+3A+A]

=7A−I+7A

=−I

Answer 2

Answer:

-i

Step-by-step explanation:

Given: a² = a

7a - (i + a)³

⇒ 7a - (i³ + a³ + 3 * i² * a + 3 * a * i²)

⇒ 7a - (i + a³ + 3a + 3a²)

⇒ 7a - (i + a * a² + 3a + 3a²)

⇒ 7a - (i + a * a + 3a + 3a) [∵ a² = a]

⇒ 7a - (i + a² + 6a)

⇒ 7a - (i + a + 6a)

⇒ 7a - (i + 7a)

⇒ 7a - i - 7a

⇒ -i

Therefore,

7a - (i + a)³ = -i

Hope it helps!