Question: Let A and B be n n matrices, x a vector in R n , and c a scalar. Prove the following matrix inequalities:

Let A and B be n × n matrices, x a vector in Rn, and c a scalar. Prove the following matrix inequalities:

a.|cA| = |c| |A|

b.|A + B| ≤ |A| + |B|

c.|Ax| ≤ |A| |x|

d.|AB| ≤ |A| |B|

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