please solution with smallest details

Q2) Let M be an R-module and ack such that ca es Consider the submodules.aM, -a). M. of H Prue that zam&4-0 CHint-Aman) 3 640 prove that the sequence 0.0MM CUM=0 , is an exact sequence where is inclusiohumumxphisun cand is the huwumexplaism delineatong RemaxXEM. (2) prove that the above request.fo.splet exact Syuence: 4o Let = Rx+ Rx+ Rx + 2xy + 2x be a free malule with the basis {xxx, xxx z and N = Rx+ RX prove that {X, Xux } is a basis for the module 5