The paper introduces a novel framework for Gaussian process (GP) inference called Blackbox Matrix-Matrix (BBMM) inference, which leverages blackbox matrix-matrix multiplication routines with kernel matrices. BBMM reduces the asymptotic complexity of exact GP inference from $\mathcal{O}(n^3)$ to $\mathcal{O}(n^2)$ by using a modified batched version of the conjugate gradients (mBCG) algorithm. This approach significantly improves the efficiency of GP inference, especially on GPU hardware. The paper also introduces a preconditioner based on the pivoted Cholesky decomposition, which further accelerates convergence. The authors demonstrate that BBMM can be easily adapted to complex GP models and scalable approximations, requiring minimal additional code. The effectiveness of BBMM is evaluated through experiments on various datasets, showing substantial speed improvements over Cholesky-based inference and comparable or better final test errors. The framework is implemented in the GPyTorch library, making it accessible for researchers and practitioners.The paper introduces a novel framework for Gaussian process (GP) inference called Blackbox Matrix-Matrix (BBMM) inference, which leverages blackbox matrix-matrix multiplication routines with kernel matrices. BBMM reduces the asymptotic complexity of exact GP inference from $\mathcal{O}(n^3)$ to $\mathcal{O}(n^2)$ by using a modified batched version of the conjugate gradients (mBCG) algorithm. This approach significantly improves the efficiency of GP inference, especially on GPU hardware. The paper also introduces a preconditioner based on the pivoted Cholesky decomposition, which further accelerates convergence. The authors demonstrate that BBMM can be easily adapted to complex GP models and scalable approximations, requiring minimal additional code. The effectiveness of BBMM is evaluated through experiments on various datasets, showing substantial speed improvements over Cholesky-based inference and comparable or better final test errors. The framework is implemented in the GPyTorch library, making it accessible for researchers and practitioners.