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

Question

Philoid · Accepted Answer

Given.

We need to find A² – 5A – 14I.

We know A² = A × A.

Now, we evaluate –5A = –5 × A.

Finally, matrix –14I = –14 × I.

The given expression is A² – 5A – 14I.

On multiplying both sides with matrix A, we get

A (A² – 5A – 14I) = O

⇒ A³ – 5A² – 14(A × I) = O

⇒ A³ – 5A² – 14A = O

⇒ A³ = 5A² + 14A

Thus, and .

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