Let A and B be arbitrary 3 times 3 matrices. State \"True\" or \"False\" for eac

Question

Let A and B be arbitrary 3 times 3 matrices. State "True" or "False" for each of the following statements. You do not need to justify your answers. (a) If |A| = -5, then A is invertible. (b) If |AB| = 0, then at least one of |A| and |B| must be zero. (c) If |A| = 0 and |B| = 0, then |A + B| = 0. (d) If |A| = 0 and |B| = 0, then |AB| = 0. (e) |3A| = 3|A|.(f) |-A| = -|A|. (g) |A^3| = |A|^3. (h) If every entry of A is positive, then |A| is positive. (i) If every entry of A is an integer, then |A| is an integer. (j) |A + B| lessthanorequalto |A| + |B|.

Explanation / Answer

a) True

b) True

c) True

d) True

e) False

f) False

g) True

h) False

i)True

j)False

I could justify my answers but it was not requested by the client.

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