Question: Can you help me with this question? Thanks. Let . | : Cmxn - R be a norm, defined for all m, n E N.

Can you help me with this question? Thanks.

Let . | : Cmxn - R be a norm, defined for all m, n E N. Show that there always exists a c > 0 such that the constant multiple | | . ||c := c| . || defines a submultiplicative norm, i.e., I| AB |lc |Allcl| B Ilc for any A e Cmxn and B E C"XP (even if | . | does not have this property)

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