Question

prove that determinant is equal to zero,where R1=[a b c d 1],R2=[b c d a 1],R3=[c d a b 1], R4=[d a b c 1],R5=[b a d c 1].

Answer 1

Consider last column. Determinant would be

[b c d a] - [a b c d] + [a b c d] - [a b c d] + [a b c d]
[c d a b] [c d a b] [b c d a] [b c d a] [b c d a]
[d a b c] [d a b c] [d a b c] [c d a b] [c d a b]
[b a d c] [b a d c] [b a d c] [b a d c] [d a b c]

Then try to find swapped columns or rows, which only change the sign of a determinant, and go from there.