There is a symmetrical block-matrix:
$M_1=\begin{pmatrix}A & 0\\ 0 & B\end{pmatrix}$
$A,B$ - symmetrical matrices
We can find the trace of this matrix $Tr(M_1)$. Can we find a new matrix $M_2$ such that $Tr(M_1)=Det(M_2[A,B])$ ?
That's such an interesting task :))
I found a special case where this is possible:
But I did not find a more general solution for symmetrical block-matrix of another dimensions.