Let b and c be two real numbers such that the numbers 3, b, c are in geometric progression. For the matrix 

$$A = \begin{bmatrix}1 & 1 & 1 \\3 & b & c \\9 & b^{2} & c^{2} \end{bmatrix}$$, if $$\text{det}\mid A \mid = 162$$, then the value of c is

A

27

B

54

C

12

D

48