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Determinant Derivative

Hard · Data Science · Quant Trader interview question · linear-algebra, matrix-calculus, derivatives, determinant

Let $X$ be an invertible $n \times n$ matrix. What is the derivative of the determinant of $X$, $\det(X)$, with respect to $X$? Express your answer using matrix notation. Remember that the derivative of a scalar with respect to a matrix is a matrix of the same size.