=∣∣
∣
∣∣√23√5√5√465√10√115√155∣∣
∣
∣∣+∣∣
∣
∣∣√3√5√5√155√103√155∣∣
∣
∣∣
=∣∣
∣
∣∣√23√5√5√2×23√5√5√2×5√5×23√5×3√5√5∣∣
∣
∣∣+∣∣
∣
∣∣√3√5√5√3√5√5√5√2√5√3√3√3√5√5√5∣∣
∣
∣∣
=∣∣
∣
∣∣√23√5√5√2×23√5√5√2×5√5×23√5×3√5√5∣∣
∣
∣∣+∣∣
∣
∣∣√3√5√5√3×5√5√5√2√5√3√3√3√5√5√5∣∣
∣
∣∣
=∣∣
∣
∣∣√23√5√5√2√23√5√5√2√5√5√23√5√3√5√5∣∣
∣
∣∣+∣∣
∣
∣∣√3√5√5√3√5√5√5√2√5√3√3√3√5√5√5∣∣
∣
∣∣
In the first determinant using C1→C1√23,C2→C2√5 and C3→C2√5
In the second determinant using C1→C1√3,C2→C2√5 and C3→C2√5
=√23√5√5∣∣
∣
∣∣111√2√5√2√5√3√5∣∣
∣
∣∣+√3√5√5∣∣
∣
∣∣111√5√5√2√3√3√5∣∣
∣
∣∣
C1→C1−C3 in the first determinant and
C1→C1−C2
5√23∣∣
∣
∣∣0110√5√20√3√5∣∣
∣
∣∣+5√3∣∣
∣
∣∣0110√5√20√3√5∣∣
∣
∣∣
=0 since one column in both the determinants are zero
Hence Proved