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Matrix multiplication and matrix inverse have the same asymptotic running time. If we denote the running time of multiplying two $n \times n$ matrices by $T_1(n)$, and that of inverting an $n \times n$ matrix by $T_2(n)$, then this means that there exist constants $A,B$ such that $$ T_1(n) \leq AT_2(n) \\ T_2(n) \leq BT_1(n). $$ However, the constants $A,B$ ...

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