Doing the computations by hand, find the determinant of the matrix \(A\).

\[ A = \begin{pmatrix} 2 & 1 & 1 & 0 \\ 1 & 2 & 1 & 2 \\ -1 & 1 & 0 & 0 \\ 1 & 2 & 0 & 1 \end{pmatrix} \]

A <- matrix(c(2, 1, 1, 0,
               1, 2, 1, 2,
              -1, 1, 0, 0,
               1, 2, 0, 1), nrow = 4, byrow = TRUE)


determinant <- det(A)

print(determinant)
## [1] -6