Question

For the matrix A = $\begin{bmatrix} 1 & 1 & 0 \\ 1 & 2 & 1 \\ 2 & 1 & 0 \end{bmatrix}$, which is correct –

• A. A³ + 3A² – I = 0
• B. A³ – 3 A² – I = 0
• C. A³ + 2A² – I = 0
• D. A³ – A² + I = 0

Answer 1

Answer: (B)

A³ – 3 A² – I = 0

Answer 2

A³–3A²–I=$\begin{bmatrix} 7 & 9 & 3 \\ 15 & 19 & 6 \\ 9 & 2 & 4 \end{bmatrix}$–$\begin{bmatrix} 6 & 9 & 3 \\ 15 & 18 & 6 \\ 9 & 12 & 3 \end{bmatrix}$

a –$\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$ = 0̃ A³ – 3A² – I = 0