CoCalc -- 246.sagews

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x := X(Rationals);;
mat := One(x)*[[-2,x],[x^2-2*x,x]];
Determinant(mat);

[ [ -2, x_1 ], [ x_1^2-2*x_1, x_1 ] ]
-x_1^3+2*x_1^2-2*x_1