$($This is a generalization of problem $4\mathrm{.}2-5$ on page $82$ of CLRS $3^{rd}$ edition.$)$

Suppose there is a method for multiplying $mm$ matrices using only $k$ multiplications $($not

assuming commutativity of multiplication of matrix elements$),$ where $n$nnmo$(n^3)k.$ Explain how $to$

recursively multiply $nn$ matrices $(wherenisan$ exact power $ofm)in$ time $o(n^3)by$ using this

method $as$ a subroutine. What $is$ the runtime $of$ your algorithm? $(Hint$: Imitate Strassen's algorithm.$)$