Let this matrix be A and cofactor of the elements be Cij
The determinant can be easily found by applying the cofactor multiplication on 3rd row(Since we have many zeroes which is easier for calculations)..
For Row 3,
det A =(-1)3+4.(1).det .—————Eqn 1
Now, expanding the cofactor C34 we have
(-1)1+2(1) det —————Eqn 2
Again expanding the cofactor C12,we will have
-1*0-(1) ——————— Eqn 3
Combine all these 3 equation to have
(-1)(1)*(-1)(1)*(-1)=-1*-1*-1 =-1