Question: True or false: If true, explain why. If false, give an explicit counterexample. (a) If det 0 then A-l exists. (b) det(2A) = 2 det

True or false: If true, explain why. If false, give an explicit counterexample.
(a) If det ‰ 0 then A-l exists.
(b) det(2A) = 2 det A.
(c) det(A -(- B) = det A + det B.
(d)

(e)

(f) det[(A + B)(A - B)] = det(A2 - B2).
(g) If A is an n x n matrix with det A = 0, then rank A (h) If det A = I and A8 = 0, then B = O.

detA-T det A det(AB-) = deta det B

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