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The problem of inverting matrices is one that occurs in some problems of practical importance. This paper introduces and evaluates the block algorithm for high performance matrix inversion on the Cell Broadband Engine (Cell/B.E.) processor. The Cell/B.E. is a heterogeneous multi-core processor on a single-chip jointly developed by Sony, Toshiba and IBM, which has a very high speed of the single precision floating-point arithmetic. The discussed matrix inversion algorithm is a combination of the block algebraic path problem algorithm and the well-known block matrix inversion algorithm based on the LU decomposition. For relatively big matrices, this combined block algorithm spends the most time in computing matrix-matrix multiplication of blocks and achieves 149.4 Gflop/s on Cell/B.E., when PPE and six SPEs of PlayStation3 are used, or 93.4% of the aggregated double (PPE) and single (SPEs) precision peak performance, which is 160.0 Gflop/s.