In $\triangle \mathrm{ABC}$, if $\left|\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right|=0$, then $\cos \mathrm{A} \cos \mathrm{B}+\cos \mathrm{B} \cos \mathrm{C}+\cos \mathrm{C} \cos \mathrm{A}=$

• A

  -1
• Correct answer
  B

  $\frac{3}{4}$
• C

  $\frac{9}{4}$
• D

  1

Hence, the correct answer is option: 'B'.