Using the properties of determinants in prove that:


Taking LHS,

Applying R1 R1 – R2, we get





[(a2 – b2) = (a – b)(a + b)]


Taking (a – 1) common from the first row, we get



Applying R2 R2 – R3, we get





Taking (a – 1) common from the second row, we get



Now, expanding along C3, we get


= (a – 1)2 [1{(a + 1) – 2}]


= (a – 1)2 [a + 1 – 2]


= (a – 1)3


= RHS


Hence, LHS = RHS


Hence Proved


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