In this paper, we present an explicit formula for the inverse and determinant in geometric (Clifford) algebras over vector spaces of dimension \(n=7\) . We generalize the concept of conjugation to basis conjugation operations, allowing us to express the determinant formula independently of any specific algebra isomorphism. This construction provides a practical computational tool for determining invertibility and calculating inverses of multivectors in geometric algebras associated with seven-dimensional vector spaces. The resulting formulas extend previous results for lower dimensions and offer new insights for applications in mathematical physics and computational geometry.