Identify the correct statements.

(A) If A is a non-sigular matrix, then $A^{-1}=\frac{|A|}{(adjA)}$

(B) If A is an invertible matrix then $\frac{1}{|A^{-1}|}=|A|$

(C) If A and B are two invertible matrices of the same order then AB is also invertible matrix and $(BA)^{-1}=A^{-1}B^{-1}$

(D) If A is an invertible matrix, then AT is also invertible and $(A^T)^{-1}=\frac{1}{(A^{-1})^T}$

Choose the correct answer from the options given below : 

(B) and (C) only

Option B is correct as $|A^n=|A|^n$ n be any integer.

$⇒\frac{1}{|A^{-1}|}=|A|$

Option C is also correct as if x, y are two matrices.

$xy = yx = 1$, then $x = y^{-1}$

Given $(BA)^{-1}=A^{-1}B^{-1}$

Multiply with BA to $A^{-1}B^{-1}$

$BAA^{-1}B^{-1}=B(AA^{-1})B^{-1}=BB^{-1}=I$

Multiply with $A^{-1}B^{-1}$ with BA

$A^{-1}B^{-1}BA=A^{-1}IA=A^{-1}A+I$

$BA(A^{-1}B^{-1})=(A^{-1}B^{-1})BA=I$

$(BA)^{-1}=A^{-1}B^{-1}$

So, statement B and C are correct.