Do administrative assistants influence the business? or their job is detached they are just managing office stuff?

Administrative assistant must be multi- talented and should do multi tasks.

Administrative assistants can influence a business by offering support to different departments example in human resource,finance Prepares invoices and payments of claims, requisitions, purchase orders and other fiscal duties.

Admin Assistant - must have the ability to assist with most things that affect the business. The Admin Assistant role is best to be seen as a progressive role.  This enables on the job learning and progression.  A competent, highly skilled Admin Assistant can be an asset for a business.  If the Admin Assistant is willing to learn and is trained well, all business challenges, goals and targets can be achieved with a good Admin Assistant.

If administrative study can determine which powers should go to which administrators .... Officials become involved in their office as a career within the hierarchal order of public service. So therefore He or She Must be able to positievly Influence the business and also do office stuffs.

It totally depends on the level where you are providing your services.

Suppose you are EA or PA of a MD or CEO, the offcourse, you have influence on business, as you are the first point to MD or CEO, and this position has tremendous power and influence in the organization also.

Suppose you are administrative assistant to GM, Mangers, then you are providing just office administration services, you do not have influence.