Let A be the `2 xx 2` matrix given by `A=[a_("ij")]` where `a_("ij") in {0, 1, 2, 3, 4}` such theta `a_(11)+a_(12)+a_(21)+a_(22)=4` then which of the following statement(s) is/are true ?

Options

A. Number of matrices A such that the trace of A equal to 4, is 5
B. Number of matrices A, such that A is invertible is 18
C. Absolute difference between maximum value and minimum value of det (A) is 8
D. Number of matrices A such that A is either symmetric (or) skew symmetric and det (A) is divisible by 2, is 5.

Explanation

To solve the problem, we need to analyze the conditions given for the matrix \( A \) and check the validity of each statement provided.

### Given:
Matrix \( A \) is a \( 2 \times 2 \) matrix represented as:
\[
A = \begin{bmatrix}
a_{11} & a_{12} \\
a_{21} & a_{22}
...