Definition. For any A∈ Mn×n(C), define the norm of A by ||A||= max{|Aij |: 1 ≤i, j≤n}.Let A,B∈ Mn×n(C). Prove the following results.(a)||A||≥0 and ||A||= 0 if and only if A=O.(b) ||cA||= |c| . ||A||for any scalar c.(c)||A+B||≤||A||+ ||B||.(d)||AB||≤n||A||||B||.

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Asked Dec 31, 2019
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Definition. For any A∈ Mn×n(C), define the norm of A by ||A||= max{|Aij |: 1 ≤i, j≤n}.

Let A,B∈ Mn×n(C). Prove the following results.

(a)||A||≥0 and ||A||= 0 if and only if A=O.

(b) ||cA||= |c| . ||A||for any scalar c.

(c)||A+B||≤||A||+ ||B||.(d)||AB||≤n||A||||B||.

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