Let G be a locally compact group equipped with the left Haar measure mG, Mn be an n×n matrix with entries in C and let L1(G,Mn) be the Banach algebra respect to the convolution products ⁎ and ⁎ℓ that consists all Mn-valued functions on G. We characterize representations of L1(G,Mn) with respect to the convolution products ⁎ and ⁎ℓ and we show that with respect to these convolutions, the obtained representations are different. Moreover, we consider the matrix-valued positive type function on G and investigate some topological properties of these functions. Finally, we consider matrix-valued Fourier transforms on Abelian locally compact groups and prove a generalisation of Bochner's Theorem for matrix-valued positive type functions.