The correct option is D None of these
Q=⎡⎢⎣abccabbca⎤⎥⎦ is an orthogoanal matrix.
Therefore according to given data,
a2+b2+c2=1 and ab+bc+ca=0
|Q|=∣∣
∣∣abccabbca∣∣
∣∣=(a+b+c)(a2+b2+c2−ab−bc−ca)
⇒|Q|=a+b+c=±1 (∵|QQT|=1)
a3+b3+c3−3abc=(a+b+c)(a2+b2+c2−ab−bc−ca)
⇒a3+b3+c3=±1+3abc
∴a3+b3+c3=±1+3p
Hence, option D.