Give an example of a 2x2 matrix whose determinant is 13.

how would i come up with numbers? is it just a random guess and check?

If all your entries are integers, the determinant is also an integer. 
For this problem, 1        0
                             0        13

For this question, you should just fix  3 values and make the 4th value an unknown and solve it.
I hope my answer helped you somehow.

I (-4, -3)

J (-4,-2)

K (-2,-2)

L (0,-4)