Question

Find the value of the following determinant.
$\left|\begin{array}{cc}2i& -3i\\ i^3& -2i^3\end{array}\right|$, where $i=\sqrt{-1}$.

Answer 1

Given, $\left|\begin{array}{cc}2i& -3i\\ i^3& -2i^3\end{array}\right|$, where $i=\sqrt{-1}$.

Expanding the determinant we get

$=2i\times (-2i^3)-(-3i)\times i^3$

$=-4i^4+3i^4$

$=-i^4$

$=-1$