here the given two eigen values are (2 + (-1)^½ ) and 3
we know determinant of a matrix is product of it's eigen values, so here determinant can't be imaginary number so there would be a value which is conjugate of the imganiry number so on multiplication it will give real number and the value will be (2 - (-1)^½ )
so now (2 + (-1)^½ ) * (2 - (-1)^½ ) == (2^2 - (-1)^½ ^2) == 4 – (-1) = 5
so final answer will be 5 * 3 = 15
|P| = 15