Question
Show that$$\left|\begin{array}{lll}1 & a & a^{2} \\a^{2} & 1 & a \\a & a^{2} & 1\end{array}\right|=\left(a^{3}-1\right)^{2}$$
Step 1
The determinant of a 3x3 matrix can be calculated as follows: $$\left|\begin{array}{lll} 1 & a & a^{2} \\ a^{2} & 1 & a \\ a & a^{2} & 1 \end{array}\right| = 1*(1*1 - a*a^{2}) - a*(a^{2}*1 - a*a) + a^{2}*(a^{2}*a - 1*a)$$ Show more…
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