What is the value of $$\left|\begin{array}{ccc}a & b & c \\ a-b & b-c & c-a \\ b+c & c+a & a+b\end{array}\right|$$ ?

The value of $$\left|\begin{array}{ccc}b+c & a & a \\ b & c+a & b \\ c & c & a+b\end{array}\right|$$ is

Let $$A, B, C, D$$ be square real matrices such that $$C^T=D A B, D^{\mathrm{T}}=A B C$$ and $$S=A B C D$$, then $$S^2$$ is equal to

$$A=\left[\begin{array}{ccc}a^2 & 15 & 31 \\ 12 & b^2 & 41 \\ 35 & 61 & c^2\end{array}\right]$$ and $$B=\left[\begin{array}{ccc}2 a & 3 & 5 \\ 2 & 2 b & 8 \\ 1 & 4 & 2 c-3\end{array}\right]$$ are two matrices such that the sum of the principal diagonal elements of both $$A$$ and $$B$$ are equal, then the product of the principal diagonal elements of $$B$$ is