Can we use DML operations in before triggers?

Now Iam confused whether we can use DML operations in before triggers or not.Can some explain me if we can use DML operations in before triggers

trigger ownerChange on Account (before insert, before update) {
    List<id> accountIdsList = new list<id>();
    list<contact> contactListToUpdate = new list<contact>();
    for(account acc : trigger.new){
        accountIdsList.add(acc.id);
    }
    list<contact> contactList = [select id from contact where accountId IN:accountIdsList ];
    for(account acc : trigger.new){
        if(acc.ownerId!=trigger.oldMap.get(acc.id).ownerId){
         for(contact con : contactList){
             con.ownerId = acc.ownerId;
             contactListToUpdate.add(con);
         }    
        }
        update contactListToUpdate;
    }
}

?

/ The trigger needs to check all the other Opportunities related to the Account of the Opportunity being updated. It should check to see if any of the Opportunities have a StageName equal to 'Closed Won ',
// if so, it should update the account Type to 'Customer'. If none of the Opportunities are closed won, the Account Type should be 'Prospect
trigger updateAccountIfOppCustomer on Opportunity (before insert, before update) {
    list<opportunity> accOpps = new list<opportunity>();
    list<id>  accountIds = new list<id>();
    for(opportunity opp:trigger.new){
        accountIds.add(opp.accountId);
    }
    list<opportunity> opps = [select id,AccountId,StageName  from opportunity where accountId IN:accountIds];
    map<id,account> accs = new map<id,account>([select id,type from account where id IN:accountIds]);
    system.debug('accs '+accs );
    for(opportunity o:opps){
            if (o.StageName == 'Closed Won'  || o.StageName == 'Customer Reseller') {
                //acc.type = 'prospect';
                accs.get(o.accountId).type='prospect';
        }
    }
    update accs.values();
}