Question

If matrix A = $\begin{bmatrix} a & b & c \\ b & c & a \\ c & a & b \end{bmatrix}$where a, b, c are real positive numbers, abc = 1 and A^T A = 1, then the value of a³ + b³ + c³ is –

• A. 3
• B. 2
• C. 4
• D. 1

Answer 1

Answer: (C)

4

Answer 2

A^T A = I Ž |A^T A| = |I| Ž |A|² = 1

Ž (a³ + b³ + c³ – 3abc)² = 1

Ž a³ + b³ + c³ – 3abc = 1

(since a, b, c are positive real number

Ž a³ + b³ + c³ ³ 3abc from AM ³ GM)

Ž a³ + b³ + c³ = 4.Hence (3) is correct answer.