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