Using properties of determinants, prove that
Applying C1→ C1 - C2
Taking out (a-1) from C1
Applying C2→ C2 - 3C3
Taking out (a-1) from C2
Expanding along R3
= (a-1)2 [0-0+1(a+1-2)]
= (a-1)2(a-1)
= (a-1)3
Hence, L.H.S = R.H.S ....Proved
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