Given : △1=∣∣
∣∣111yzzxxyxyz∣∣
∣∣
Taking transpose of above determinant, we get
△1=∣∣
∣∣1yzx1zxy1xyz∣∣
∣∣
Now multiplying x in R1,y in R2 and z in R3, we get
△1=1xyz∣∣
∣
∣∣xxyzx2yxyzy2zxyzz2∣∣
∣
∣∣
⇒△1=xyzxyz∣∣
∣
∣∣x1x2y1y2z1z2∣∣
∣
∣∣
Now interchanging C1 and C2, we get
△1=(−1)∣∣
∣
∣∣1xx21yy21zz2∣∣
∣
∣∣=−△
∴△1+△=0