1. ## Matrix transformation

If we want:

$\frac{1}{3} \begin{bmatrix} 1 & 1 & 1 \\ 1 & a & a^2 \\ 1 & a^2 & a \end{bmatrix} = \frac{1}{3} \begin{bmatrix} 1 & 1 & 1 \\ 1 & b^2 & b \\ 1 & b & b^2 \end{bmatrix}$

And $\displaystyle a = e^{\frac{2\pi i}{3}}$, how much is $\displaystyle b$ to fulfill the condition?

So if I cancel $\displaystyle \frac{1}{3}$on both sides and try to get the inverse of one matrix I don't get $\displaystyle b = e^{\frac{-2\pi i}{3}}$ which is correct.

Thanks for the help.

2. ## Re: Matrix transformation

Two matrices are equal only if they have the same dimensions and then all corresponding elements are equal.

So here, you need
a = b^{2}
and
b = a^{2}
.

3. ## Re: Matrix transformation

Ok, maybe I don't understand, can you extrapolate thinking because the answer is $\displaystyle b = e^{\frac{-2\pi i}{3}}$. I don't know how do we get to there, do you see the problem?

4. ## Re: Matrix transformation

$\displaystyle a^{2} = e^{\frac{4\pi\imath}{3}}=e^{\frac{-2\pi\imath}{3}}$