In our real life, the bipolar fuzzy theory is a core feature to be considered positive information represents what is possible or preferred, while negative information represents what is forbidden or surely false. In this paper, we introduce the bounded sum and bounded product operations on bipolar fuzzy matrices and study the properties. We intend to construct an algebraic structure by proving various algebraic properties on bounded sum and bounded product over bipolar fuzzy matrices. Finally, we construct a commutative monoid on a bounded sum and a bounded product over bipolar fuzzy matrices