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###### Let $A$ be a nondefective $n \times n$ matrix with diagonalizing matrix $X .$ Show that the matrix $Y=\left(X^{-1}\right)^{T}$ diagonalizes $A^{T}$

Let $A$ be a nondefective $n \times n$ matrix with diagonalizing matrix $X .$ Show that the matrix $Y=\left(X^{-1}\right)^{T}$ diagonalizes $A^{T}$

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