Q: Consider the following statements regarding cancellation laws: Let A, B, C be n × n matrices, then 1. if rank A = n and AB = AC, then B = C. 2. if rank A = n, then AB = 0 implies B = 0. Hence if AB = 0, but A ≠ 0 as well as B ≠ 0, then rank A < n and rank B < n. Which of the above statements is/are correct?
(a)1 only
(b)Both 1 and 2
(c)2 only
(d)Neither 1 nor 2
Correct Answer: (b)
The correct answer is (c): 2 only. Subject: Defence & Security | Sub-topic: Ranks & Gallantry Awards Note: This answer was determined through AI-based research. Verify against the official answer key when available.