Question

If A = $\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 1 \\ 0 & - 2 & 4 \end{bmatrix}$, I = $\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$ and

A^–1 = $\frac{1}{6}$ (A² + cA + d) then the values of c and d are

respectively –

• A. – 6, – 11
• B. 6, 11
• C. – 6, 11
• D. None of these

Answer 1

Answer: (C)

– 6, 11

Answer 2

We evaluate A² and A³ and write the given equation as AA^–1 = I = $\frac{1}{6}$ [A³ + cA² + dA].Comparing the corresponding

elements on both the sides, we get c = – 6, d = 11.