Developed Gemm autodiff pullback support within the ferdymercury/root repository, focusing on enabling differentiable Gemm workflows for TMVA SOFIE integration. The work involved implementing a custom Gemm_Call_pullback in C++ to handle the backward pass of the Gemm operation, which is essential for automatic differentiation in machine learning models. To ensure correctness and maintainability, comprehensive test coverage was added through TestGemmDerivative.cxx, verifying the accuracy of computed derivatives. This contribution strengthened gradient-based optimization capabilities and improved the reliability of autodiff features related to linear algebra operations, with an emphasis on robust testing practices and integration into existing machine learning infrastructure.