$4\mathrm{.}4-5$ If mh $($t$)$ is the Hilbert transform of m$($t$),$ then

$($a$)$ Show that the Hilbert transform of mh$($t$)$ is $-$m$($t$).$

$($b$)$ Show also that the energies of m$($t$)$ and mh$($t$)$ are identical.