EXM.1.AHL.TZ0.34

pestleMathematicsAIHLPaper 1EXM· ahl-1-14-introduction-to-matricessource ↗

The square matrix X is such that X³ = 0. Show that the inverse of the matrix (I – X) is I + X + X².

Markscheme / solution

For multiplying (I – X)(I + X + X²) M1

= I² + IX + IX² – XI – X² – X³ = I + X + X² – X – X² – X³ (A1)(A1)

= I – X³ A1

= I A1

AB = I ⇒ A^–1 = B (R1)

(I – X) (I + X + X²) = I ⇒ (I – X)^–1 = I + X + X² AG N0

[5 marks]

Examiners’ report

[N/A]