The studies involving system of bicomplex numbers have significant role in the theoretical research work of various scientific disciplines like linear algebra, functional analysis, digital signal processing, and quantum mechanics. A commutative substitute for the system of quaternions is provided by the system of bicomplex numbers. In contrast to the system of quaternions that produce a division algebra without the commutative property, the system of bicomplex numbers is commutative but has divisors of zero. In this article, we investigate some sufficient conditions of hyperbolic positive matrices which are special matrices with bicomplex number. We propose a sufficient condition for the principal submatrices of a matrix to be hyperbolic positive. In order for a matrix to be hyperbolic positive under matrix multiplication, we explore a few necessary and sufficient conditions. Under several matrix products such as Kronecker product, Hadamard product, and Frobenius inner product, we establish that being hyperbolic positive is sufficient for the resulting matrix to be hyperbolic positive.