(a) Metal M has the formula , from which it is clear that the
valency of M = +3
valency of O = -2
Since M is in the third period, its outer most/third shell will have three valence electrons which will give it a configuration as 2, 8, 3.
So, the atomic number of the M = 13
Hence, M will be aluminium and its formula will be .
(b) Valency of metal M is +3 so it will form MCl3 type compound with alkaline earth metals. Since M is aluminium, the compound will be AlCl3.
(c) The atomic number of the M = 13 which means that the metal M will be aluminium.