Let A be an n x n matrix. Show that the determinant of A is the...

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Let A be an n x n matrix. Show that the determinant of A is the product of its eigenvalues (where repeated eigenvalues are counted multiple times). (Hint: You may wish to use the Fundamental Theorem of Algebra, which states that any polynomial Q(x) of positive degree can be factorized as Q(x) = c(x1)(x-2)... (xrn), where c, T,...", are complex numbers.) Let A be an n x n matrix. Show that the determinant of A is the product of its eigenvalues (where repeated eigenvalues are counted multiple times). (Hint: You may wish to use the Fundamental Theorem of Algebra, which states that any polynomial Q(x) of positive degree can be factorized as Q(x) = c(x1)(x-2)... (xrn), where c, T,...", are complex numbers.)