restart:
with(linalg):
A:=matrix(3,3,[-2,1,9,-4,2,8,-1,4,-5]);
PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRiciIiMiIiU2JEYmRiciIio2JEYmRipGJjYkRipGJyIiKTYkRipGJiEiJTYkRidGJiEiIjYkRiZGJiEiIzYkRidGJyEiJjYkRipGKkYq
det(A);
ISNx
M:=matrix(3,3,[-42,28,-14,-41,19,-7,-10,20,0]);
PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRiciIiMiIz82JEYmRichIzk2JEYmRioiI0c2JEYqRichIig2JEYqRiYhI1Q2JEYnRiYhIzU2JEYmRiYhI1U2JEYnRiciIiE2JEYqRioiIz4=
C:=matrix(3,3,[]);
PTYiNiQ7IiIiIiIkRiVFXFtsIQ==
for i from 1 to 3 do
for j from 1 to 3 do
C[i,j]:=(-1)^(i+j)*M[i,j]:
end do:
end do:
print(C);
SSJDRzYi
transpose(C);
PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRiciIiMiIig2JEYmRichIzU2JEYmRioiI1Q2JEYqRichIz82JEYqRiYhI0c2JEYnRiYhIzk2JEYmRiYhI1U2JEYnRiciIiE2JEYqRioiIz4=
evalm(1/det(A)*transpose(C));
PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRiciIiMjISIiIiM1NiRGJkYnI0YmIiIoNiRGJkYqIyEjVCIjcTYkRipGJyNGKkYwNiRGKkYmI0YqIiImNiRGJ0YmI0YmRjk2JEYmRiYjRidGOTYkRidGJyIiITYkRipGKiMhIz5GNA==
inverse(A);
PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRiciIiMjISIiIiM1NiRGJkYnI0YmIiIoNiRGJkYqIyEjVCIjcTYkRipGJyNGKkYwNiRGKkYmI0YqIiImNiRGJ0YmI0YmRjk2JEYmRiYjRidGOTYkRidGJyIiITYkRipGKiMhIz5GNA==
rref(A);
PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRiciIiMiIiE2JEYmRidGKzYkRiZGKkYrNiRGKkYnRis2JEYqRiZGKzYkRidGJkYrNiRGJkYmRiY2JEYnRidGJjYkRipGKkYm
A:=matrix(3,3,[2,-3,4,0,6,8,0,-5,1]);
PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRiciIiMhIiY2JEYmRiciIiU2JEYmRiohIiQ2JEYqRiciIik2JEYqRiYiIiE2JEYnRiZGMzYkRiZGJkYqNiRGJ0YnRiY2JEYqRioiIic=
det(A);
IiMjKg==
A1:=matrix(3,3,[2,-3,4,0,6,8,0,0,1]);
PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRiciIiMiIiE2JEYmRiciIiU2JEYmRiohIiQ2JEYqRiciIik2JEYqRiZGKzYkRidGJkYrNiRGJkYmRio2JEYnRidGJjYkRipGKiIiJw==
det(A1);
IiM3
A2:=matrix(3,3,[2,300,Pi,0,6,exp(1),0,0,1]);
PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRiciIiMiIiE2JEYmRidJI1BpRyUqcHJvdGVjdGVkRzYkRiZGKiIkKyQ2JEYqRictSSRleHBHNiRGLkkoX3N5c2xpYkdGIzYjRiY2JEYqRiZGKzYkRidGJkYrNiRGJkYmRio2JEYnRidGJjYkRipGKiIiJw==
det(A2);
IiM3
B:=matrix(4,4,[2,-4,6,8,0,-3,2,-1,0,0,1,3,0,0,0,4]);
PTYiNiQ7IiIiIiIlRiVFXFtsMTYkIiIkIiIjIiIhNiRGJkYqIiInNiRGJkYrISIlNiRGK0YqRis2JEYrRichIiI2JEYrRiZGLDYkRipGJkYsNiRGJ0YnRic2JEYqRidGKjYkRiZGJkYrNiRGKkYqRiY2JEYnRipGLDYkRidGK0YsNiRGK0YrISIkNiRGJ0YmRiw2JEYmRiciIik=
det(B);
ISND