Question

Let A, B, C be three square matrices of the same order, such that whenever AB = AC then B = C, if A is –

• A. Singular
• B. Non-singular
• C. Symmetric
• D. Skew-symmetric

Answer 1

Answer: (B)

Non-singular

Answer 2

If A is non-singular, A^–1 exists.

Thus, AB = AC ̃ A^–1(AB) = A^–1 (AC)

̃ (A^–1A) B = (A^–1 A) C ̃ IB = IC

̃ B = C.