Substitute into the equation respectively:

(A)(A 1+A2)A = A 1A+A2A = 2B。 This option is wrong.

(B)(A 1-A2)A = A 1A-A2A = B-B = 0。 This option is also wrong.

(c) (k1a1+k2a2) a = k1a1a+k2a = k1b+k2b = (k1+k2) b.

(d) refer to option c, which is obviously wrong.

The final answer is C.