When two determinants are added each of the corresponding elements gets added.

Here we can split the LHS determinant as



For the determinant u perform the following transformation R1 R3 (i.e. interchange 1st row with 3rd row)


When two particular rows/columns of a determinant are interchanged the value becomes negative 1 times the original value.



R1 R2 (i.e. interchange 1st row with 2nd row)




R1 R3 (i.e. interchange 1st row with 3rd row)



R1 R2 (i.e. interchange 1st row with 2nd row)



LHS = RHS



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