Question

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

• A. $1+a^2+b^2+c^2$
• B. $1-a^2+b^2+c^2$
• C. $1+a^2+b^2-c^2$
• D. $1+a^2-b^2+c^2$

Answer 1

The correct option is A $1+a^2+b^2+c^2$

$\left|\begin{array}{ccc}1& a& b\\ -a& 1& c\\ -b& -c& 1\end{array}\right|=1(1+c^2)-a(-a+bc)+b(ac+b)=1+a^2+b^2+c^2$.