Which of the following statements are correct?
(A) Inverse of a matrix, if it exists, is unique
(B) $(kA)'=-KA'$ (where $k$ is any real number)
(C) For an invertible matrix $A$. $(A^{-1})^{-1}= A$
(D) For an invertible matrix $A$. $(A')^{-1}= (A^{-1})'$
Choose the correct answer from the options given below.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A), (C) and (D) only **
(A) Inverse of a matrix is unique → True.
(B) $(kA)' = -kA'$ → False. Correct rule: $(kA)' = kA'$ (transpose does not change sign).
(C) $(A^{-1})^{-1} = A$ → True.
(D) $(A')^{-1} = (A^{-1})'$ → True (transpose of inverse = inverse of transpose).
Correct statements: (A), (C), (D)