Answer
a) False
b) False
Work Step by Step
a) If supply or demand are perfectly inelastic, and a tax is added to the good, there is no effect on the quantity of the good (or the deadweight loss). However, there is tax revenue when the good is sold.
b) If a tax is imposed completely on sellers, then consumers don't pay any of the tax. However, since sellers would have to pay all of the tax, sellers would not produce any of the good. Since no goods would be produced, there would be no tax revenue. However, there is deadweight loss since the quantity sold is zero.