Which of the following statements are correct ?
(A) $|A'|=|A|$ where A is the transpose of matrix A
(B) If $A=[a_{ij}]_{3×3},$ then $|4A|=64|A|$
(C) $|A|=|adj\, A|^{n-1},$ where n is the order of the matrix
(D) If A is an invertible matrix of order 2, then $det(A^{-1})$ is equal to $\frac{1}{det(A)}$
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 1
The correct answer is option (1) → (A), (B), (D) Only
(A), (B), (D) are already correct
C → incorrect
it should be $|Adj\,A|=|A|^{n-1}$
instead of $|A|=|Adj\,A|^{n-1}$