Let $\mathrm { A } = \left[ a _ { i j } \right]$ and $\mathrm { B } = \left[ b _ { i j } \right]$ be two $3 \times 3$ real matrices such that $b _ { i j } = ( 3 ) ^ { ( i + j - 2 ) } a _ { i j }$, where $i , j = 1,2,3$. If the determinant of B is 81, then determinant of A is\\
(1) $\frac { 1 } { 3 }$\\
(2) 3\\
(3) $\frac { 1 } { 81 }$\\
(4) $\frac { 1 } { 9 }$