Find inverse matrix for Vandermonde matrix using Cramer's rule

Asked Apr 21 '17 at 01:20

Active Apr 21 '17 at 06:31

Viewed 229 times

I want to prove that I can find the inverse matrix for a Vandermonde matrix using Cramer's rule.

Let $A$ be a Vandermonde matrix, and $b$ the first column of the identity matrix $I$.

When I solve $Ax=b$ with Cramer's rule, is it true that $x$ is the first column in $A^{-1}$?

So I get matrix $X$, and $AX = I$.

Unfortunately, I don't know whether it is right or not that $XA = I$?

edited Apr 21 '17 at 06:31

asked Apr 21 '17 at 01:20

Shmuser

You may be interested in proofs that $AX=I\implies XA=I$ when $A$ and $X$ are $n$-by-$n$ matrices: https://math.stackexchange.com/questions/3852/if-ab-i-then-ba-i – Jonas Meyer Apr 21 '17 at 06:41

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