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Let $A = [a_{ij}]$ and $B = [b_{ij}]$ be two $3 \times 3$ real matrices such that $b_{ij} = (3)^{(i+j-2)}a_{ij}$, where $i, j = 1, 2, 3$. If the determinant of $B$ is $81$, then the determinant of $A$ is:
(1) $1/3$
(2) $3$
(3) $1/81$
(4) $1/9$
BETA
