If then find A 2 – 5A – 14I. Hence, obtain A 3 .

Question

Philoid · Accepted Answer

Given, A =

∴ A² =

By matrix multiplication we can write:

A² =

⇒ A² = …(1)

As we have to find: A² – 5A – 14I

∴ A² – 5A – 14I =

⇒ A² – 5A – 14I =

⇒ A² – 5A – 14I = = O

We need to find value of A³ using the above equation:

Now we have,

A² – 5A – 14I = O

⇒ A² = 5A + 14I

Multiplying with A both sides

⇒ A².A = 5A.A + 14IA

⇒ A³ = 5A² + 14A

Using equation 1 we get:

⇒ A³ =

If then find A2 – 5A – 14I. Hence, obtain A3.