Matrix multiplied by inverse is not giving correct answer

The inverse of a matrix multiplied by itsef should give an identity matrix but the result I get is this: [0 0 0; -4 0 0; -4 0 0]

[Vladimir Sovkov]

Try

det(sym(a))

It is strict zero. Hence, there is no inverse matrix indeed. Matlab is quite correct here.

Answer 1

[David Goodmanson]

Matlab is telling you the answer, that the matrix (call it M) is close to singular or badly scaled (singular in this case). M has a ridiculously small condition number of 2e-18. It doesn't have an inverse, and the one it comes up with is due to numerical precision issues.

If M had an inverse, it would be impossible to have a nonzero column vector u such that M*u = 0. However,

M = [1 2 3;4 5 6;7 8 9]
M*[1; -2; 1]
ans =
     0
     0
     0