Find the determinant of A=(1ab−a1c−b−c1)A = \begin{pmatrix} 1 & a & b \\ -a & 1 & c \\ -b & -c & 1 \end{pmatrix}A=1−a−ba1−cbc1.
1+a2+b2+c21+a^2+b^2+c^21+a2+b2+c2
1−a2−b2−c21-a^2-b^2-c^21−a2−b2−c2
1+a+b+c1+a+b+c1+a+b+c
0