Squary Matrices

Let $P = [a_{ij}]$ be a $3 \times 3$ matrix and let $Q = [b_{ij}]$ be another $3\times 3$ matrix such that $b_{ij}= 2^{i+j} a_{ij}$ , where $i,j \in [1,3]$ . Given that $\det (P) = 2$ , find $\det (Q)$ . If $\det (Q) = 2^n$ , where $n$ is a natural number, input $n$ .

Notation: $\det (X) = |X|$ denotes the determinant of $X$ .