This chapter investigates the properties and calculation for Boolean determinant and Boolean equation over the Boolean field \(\mathcal {B}\) . Firstly, the concepts of Boolean determinant and Boolean equation are introduced. After that, the properties of Boolean determinant are explored similar to the determinant in linear algebra. Finally, by means of elementary transformations for Boolean equation, the properties of solutions for a Boolean equation over the Boolean field \(\mathcal {B}\) are studied.