Stunned

If $7\log (t_{r}(A)) \leq 4 \log 7$ where $A$ is a diagonal matrix of order 7 with positive entries and $|A|=7^{-3}$ then $t_{r}(A^{2}) =p$ ,

Find $p^{6}$

Note: $t_{r}(A)$ denotes trace of matrix A.