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Given the matrix
$$
A =
\begin{bmatrix}
1&1&1&1\\
a&b&c&d\\
a^{2}&b^{2}&c^{2}&d^{2}\\
a^{3}&b^{3}&c^{3}&d^{3}
\end{bmatrix}
$$
How can I prove that $\det(A)=(d-c)(d-b)(d-a)(c-b)(c-a)(b-a)$ ?
And as a second question, what is the general formula for this type of matrix and how can I prove i?
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