Evaluate the determinant for the following matrix [-2 5 4 3]

I'm assuming that the matrix is a 2 x 2 matrix. 
| -2     5 |
|  4     3 |

To determine the determinant of the matrix, we simply find the difference of the product of its diagonals. 

| a  b |
| c  d |  → ad - bc = determinant

| -2   5 |
|  4   3 | → [(-2) * 3] - (5*4) = -6 - 20 = -26

Even though the determinants are place in an absolute-value bars, they can still be negative form.

 The determinant in the above matrix is -26.