Firstly, multiply and divide R1, R2, R3 by x, y, z respectively, we get
[rearrange the terms]
Taking xyz common from the first and second column, we get
Applying C3→ C3 + C1, we get
Taking common (xy + yz + xz) common from C3, we get
If any two columns (or rows) of a determinant are identical (all corresponding elements are same), then the value of determinant is zero.
Here, C2 and C3 are identical.
∴ LHS = RHS
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