Let A and B be arbitrary 3×3 matrices. State “True” or “False” for each of the f

Question

Let A and B be arbitrary 3×3 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) |A3 | = |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| |A| + |B|.

Explanation / Answer

a) true

b) true

c) false

d) true

e) false

f) true

g) true

h) false

i) true

j) true

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