I have seen a number of places in literature claim that the complexity of multiplying two nxn matrices is equivalent to the complexity of being able to take their inverse. (assuming square invertible matrices of course)
While one part of that seems clear and well documented on the internet (how to use a fast multiplication algorithm to get the inverse at equivalent speed), I am having trouble understanding why the reverse of that is true. (ie given two matrices and their inverses or an algorithm that can quickly compute the inverse find the product efficiently)
Is there a known algorithm that allows one to quickly compute the product of two matrices when their inverses are known?