Which of the following are correct?
(A) For a square matrix A, if $A^3 = I$, then $A^{-1} = A^2$.
(B) The determinant of only a square matrix can be defined.
(C) If A is a square matrix of order 3, then the number of minors of the matrix A is 3.
(D) If A and B are two non-singular matrices of the same order, then $(AB)^{-1}= B^{-1}A^{-1}$.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A), (B) and (D) only
(A) If $A^3=I$, then multiplying both sides by $A^{-1}$ gives $A^2=A^{-1}$. Correct.
(B) Determinant is defined only for square matrices. Correct.
(C) For a $3\times 3$ matrix, the total number of minors = $9$ (one for each element). Hence 3 is wrong.
(D) $(AB)^{-1}=B^{-1}A^{-1}$. Correct.