If A and B are any two square matrices of the same order, then

(AB)' = B' A'

The correct statement is:

The correct answer is (3) (AB)' = B' A'

1. (AB)' = A' B' is not generally true. The transpose of a product of matrices is the product of their transposes in the reverse order.

2. adj(AB) = adj(A) adj(B) is not generally true. The adjugate (or adjoint) of a product of matrices is not the product of their adjugates.

3. (AB)' = B' A' is the correct statement. The transpose of a product of matrices is the product of their transposes in the reverse order.

4. AB = O ⇒ A = O or B = O is not generally true. If \(A\) or \(B\) is not invertible, it is possible to have \(AB = O\) without \(A\) or \(B\) being the zero matrix.

Therefore, option (3) is the correct one.