Which of the following statement are correct?
(A) \(A=\left[a_{i j}\right]_{n \times n}\) is a diagonal matrix if \(a_{i j}=0\) when \(i=j\)
(B) A square matrix \(A=\left[a_{i j}\right]\) is called a symmetric matrix if \(a_{i j}=a_{j i}\) for all \(i, j\)
(C) A square matrix \(A=\left[a_{i j}\right]\) is called a skew-symmetric matrix if \(a_{i j}=-a_{j i}\) for all \(i, j\)
(D) For every square matrix A, there exist an identity matrix of the same order such that \(I A=A I=I\)
Choose the correct answer from the options given below:

1. A (A), (B) and (C) only
2. B (B), (C) and (D) only
3. C (A) and (C) only
4. D (B) and (C) only