Consider the matrix AAA where Aij=(i+j−2i−1)A_{ij} = \binom{i+j-2}{i-1}Aij=(i−1i+j−2) for 1≤i,j≤31 \leq i, j \leq 31≤i,j≤3. Compute det(A)\det(A)det(A).
111
000
222
−1-1−1