"Testing cofactor"

clear

T = cofactor(((1,2),(3,4)),1,1)
check(T = 4)
T = cofactor(((1,2),(3,4)),1,2)
check(T = -3)
T = cofactor(((1,2),(3,4)),2,1)
check(T = -2)
T = cofactor(((1,2),(3,4)),2,2)
check(T = 1)
T = cofactor(((1,2,3),(4,5,6),(7,8,9)),1,2)
check(T = 6)

A = ((a11,a12),(a21,a22))
B = A
for(i,1,2,for(j,1,2,B[i,j] = cofactor(A,i,j)))
check(B = transpose(adj(A)))

A = ((a11,a12,a13),(a21,a22,a23),(a31,a32,a33))
B = A
for(i,1,3,for(j,1,3,B[i,j] = cofactor(A,i,j)))
check(B = transpose(adj(A)))

A = ((A11,A12),(A21,A22))
B = ((0,0),(0,0))
for(i,1,2,for(j,1,2,B[j,i] = cofactor(A,i,j)))
check(adj(A) == B)

A = ((A11,A12,A13),(A21,A22,A23),(A31,A32,A33))
B = ((0,0,0),(0,0,0),(0,0,0))
for(i,1,3,for(j,1,3,B[j,i] = cofactor(A,i,j)))
check(adj(A) == B)
