Oxidation states of......

Zn + 2Mn02 + 2NH4Cl = ZnCl2 + Mn2O3 + 2NH3 + H2O

I have worked out that Zn gains two electrons therefore is the oxidized element (reducing agent)
and Mn loses an electron therefore is reduced (oxidizing agent)
Can someone confirm that I am on the right track?? Thank You

Oxidation states of Zn in Zn = 0
Oxidation states of Zn in ZnCl2 = +2

Oxidation states of Mn in MnO2 = +4
Oxidation states of Mn in Mn2O3 = +3