Consider the matrix A = [[1,a,a^2],[1,b,b^2],[1,c,c^2]] Show that A is invertible if a, b, c are different numbers.
For A to be invertible its determinant must be zero, since
`A^(-1) = 1/det(A)C^T`
where `C` is the cofactor matrix of A. If det(A) is zero, then we are dividing by zero and the inverse matrix is thus undefined.
Through calculation we find that det(A) = |A| equals
If any element of this is zero, then the determinant of A is zero and A is non-invertible. Therefore we must have `a != b`, `a !=c` and `b!=c` .
In other words, for the matrix A to be invertible none of a, b and c can be the same numbers.