Let \(A = \begin{bmatrix} 0 & 1 & -1 \\ 1 & 3 &2 \\ 4 & 1 &-2\end{bmatrix}\). Let \(i = 2\) and \(j = 3\).
What is the value of \((-1)^{i+j}\det(A(i \mid j))\)?
The answer is 4.
\((-1)^{i+j}\det(A(i \mid j)) = (-1)^{2+3}\det( A(2 \mid 3)) = - \left| \begin{array}{cc} 0 & 1\\ 4 & 1\end{array} \right| = - (0 - 4) = 4\).