Prove the following

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