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   why multi core power cable we are using Steel wire armour and single core power cable we are using Aluminium wire armour?

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Steel wire armour is only used on multicore versions of the cable. A multicore cable, as the name suggests, is one where there are a number of different cores. When cable has only one core, aluminium wire armour (AWA) is used instead of steel wire. This is because the aluminium is non-magnetic. A magnetic field is produced by the current in a single core cable. This would induce an electric current in the steel wire, which could cause overheating.

Aluminium is non-magnetic. Hence, there would not be any induced currents in the armour due to the current flowing in the main conductor.
Because, in multi-core cables, the resultant or the residual flux available for linking with the armour would be zero. And, in single core cables, there would not be any compensating flux from any neighbouring core and thus there would be appreciable residual flux available for linking with the armour and, if the armour is made of a magnetic material, such a resultant flux would induce voltages in the armour which would cause circulating currents, leading to heating and damage of the armour and the cable.