dear haripriya,
1- if the company following matrix org. structure then every manager is responsible to all top managers.
2- there is no any specific responsibilities for matrix manager ( matrix manager is not the any profile or post or job)
e.g . if you are the HR manager and you are reporting to HR head, Finance head,Marketing head and top mgmt. you are the matrix manager.
any manger fall under matrix call matrix manager. and that can be any one
satish