Show that $$ A=\left[\begin{array}{ll} \alpha+i \gamma & -\beta+i \delta \\ \beta+i \delta & \alpha-i \gamma \end{array}\right] $$ is unitary if $\alpha^{2}+\beta^{2}+\lambda^{2}+\delta^{2}=1$
Added by Paula B.
Step 1
Step 1:** The determinant of matrix A is given by: $$\text{det}(A) = (\alpha + i\gamma)(\alpha - i\gamma) - (-\beta + i\delta)(\beta + i\delta)$$ $$\text{det}(A) = \alpha^2 + \gamma^2 + \beta^2 + \delta^2$$ ** Show more…
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