The objective of this paper is to apply the concept of intuitionistic fuzzy matrices and pythagorean fuzzy matrices to q-rung orthopair fuzzy matrices. In this paper, we introduce the Hamacher operations of q-rung orthopair fuzzy matrices and prove some desirable properties of these operations, such as commutativity, idempotency and monotonicity. Further, we prove De Morgan's laws over complement for these operations. Then we constructed the scalar multiplication $({n._{h}}A)$ and exponentiation $(A^{\wedge_{h}n})$ operations of q-rung orthopair fuzzy matrices and investigate their algebraic properties. Finally, we prove some properties of necessity and possibility operators of q-rung orthopair fuzzy matrices.