Orthogonality of filter impulse response to its even shift
Since this is clearly homework, let's help you with hints:

The set of  tricks for such problems is typically pretty limited; try (and that's really what solves the issue)


Multiplying the equation with elements from your right-hand term from left and/or right, so that identity matrices form.
Writing your matrix/operator property down as structure of your matrix
applying transposes, and hermitians until things happen.