[1] Interchange leading diagonal elements:

math expression

[2] Change signs of the other 2 elements:

math expression

[3] Find |A|

Remember that our original matrix (from the question) is

A = math expression

So the determinant of A is given by:

|A| = math expression = 14 - 12 = 2

[4] Multiply result of [2] by math expression

 

math expression

Is it correct?

Check:

math expression