Question: Let M (n) be the time to multiply two n n matrices, and let S (n) denote the time required to square an n

Let M (n) be the time to multiply two n × n matrices, and let S (n) denote the time required to square an n × n matrix. Show that multiplying and squaring matrices have essentially the same difficulty: an M(n)-time matrix-multiplication algorithm implies an O(M (n))-time squaring algorithm, and an S(n)-time squaring algorithm implies an O(S (n))-time matrix-multiplication algorithm.

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