Matrices And Determinants

$\left|\begin{array}{ccc}a+1 & b+1 & c+1 \\ a^2+1 & b^2+1 & c^2+1 \\ 1 & 1 & 1\end{array}\right|$

$\left|\begin{array}{ccc}a-b & b-c & c \\ a^2-b^2 & b^2-c^2 & c^2 \\ 0 & 0 & 1\end{array}\right|$

$\left|\begin{array}{ccc}a(a+1) & b(b+1) & c(c+1) \\ a+1 & b+1 & c+1 \\ -1 & -1 & -1\end{array}\right|$

$\left|\begin{array}{ccc}a+b & b+c & c+a \\ a^2+b^2 & b^2+c^2 & c^2+a^2 \\ 2 & 2 & 2\end{array}\right|$