Let A =[ a_i j] and B =[ b_i j] be two 3 × 3 real matrices such that b_i j=(3)^(i+j-2) a_j i, where i, j=1,2,3. If the determinant of B is 81, then…

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