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True or false; for each of the statements below, state whether they are true or false....

True or false; for each of the statements below, state whether they are true or false. If false, give an explanation or example that illustrates why it's false.

(a) The matrix A = [1 0] is not invertible.
                              [1 -2]

(b) Let B be a matrix. The rowspaces row (B), row (REF(B)) and row (RREF(B)) are all equivalent.

(c) Let C be a 5 x 7 matrix with nullity 3. The rank of C is 2.

(d) Let D be an n x n matrix and On be the nxn zero matrix. If d^2 = On, then D = On.

(e) Let A, B, and C be invertible nxn matrices. Then det(ABC) = (det(2B)det(3C^t)) / det(6a^-1)

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