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Adjoint of matrix A, is the transpose of the matrix of cofactors of elements in A.  When we multiply A with Adjoint (A), we have either 0,

If A is of order n X n matrix, then  the matrix product  [ A ] [ Adj A ] is a diagonal matrix with determinant of matrix A as each element and all the non diagonal elements are zero.

Hence,    determinant of  [ A ] [ Adj A ]  is | A |^n.

       Hence,    Determinant of A =  (343)^1/3  = 7

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