Using the property of determinants and without expanding.
∣∣ ∣∣276538755986∣∣ ∣∣=0
Let A=∣∣ ∣∣276538755986∣∣ ∣∣=∣∣ ∣∣2765−633875−725986−81∣∣ ∣∣ (using C3→C3−9C2)
=∣∣ ∣∣272383595∣∣ ∣∣=0 [Since, the two columns C3 and C1 are identical]
Using the property of determinants and without expanding. ∣∣ ∣∣a−bb−cc−ab−cc−aa−bc−aa−bb−c∣∣ ∣∣=0
∣∣ ∣∣b+cq+ry+xc+ar+pz+xa+bp+qx+y∣∣ ∣∣=2∣∣ ∣∣apxbqycrz∣∣ ∣∣
Using the property of determinants and without expanding. ∣∣ ∣∣xax+ayby+bzcz+c∣∣ ∣∣=0