Let A =[ a_i j]= [log_5 128, log_4 5; log_5 8, log_4 25]. If A_i j is the cofactor of a_i j, C_i j=Σ_k =1^2 a_i k A_j k, 1 ≤ i, j ≤ 2, and C =[ C_i…

Let $\displaystyle \mathrm{A}=\left[\mathrm{a}_{i j}\right]=\left[\begin{array}{cc}\log _5 128 & \log _4 5 \\ \log _5 8 & \log _4 25\end{array}\right]$. If $\displaystyle \mathrm{A}_{i j}$ is the cofactor of $\displaystyle \mathrm{a}_{i j}, \mathrm{C}_{i j}=\sum_{\mathrm{k}=1}^2 \mathrm{a}_{i \mathrm{k}} \mathrm{A}_{j \mathrm{k}}, 1 \leq i, j \leq 2$, and $\displaystyle \mathrm{C}=\left[\mathrm{C}_{i j}\right]$, then $\displaystyle 8|\mathrm{C}|$ is equal to: