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A is square matrix of order 2 such that ...

`A` is square matrix of order `2` such that `A A^(T)= I` and `B` is non-singular square matrix of order `2` and period `3`. If `det (A)!=det(B),` then value of `sum_(r=0)^(20)det(adj(A^(r)B^(2r+1)))` is (where `A^(T)` denotes the transpose of matrix `A` )

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