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I would like to emulate what Wolfram Alpha does in Mathematica. Can you help me?

WolframAlpha["Det[{{3,-1,4,6},{2,-3,1,13},{4,-2,7,12},{0,-1,0,9}}]",
             {{"Result", 2}, "Content"}, PodStates -> {"Result__Step-by-step solution"}]
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    $\begingroup$ This answer can be modified a bit so that it computes the determinant step-by-step. $\endgroup$ Feb 25, 2021 at 6:10
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    $\begingroup$ What do you mean by "step-by-step calculation of determinant"? The command from the question works in 12.2. The matrix is reduced to the upper-triangular form preserving the value of its determinant and then its deteminant equals the product of the diagonal elements. $\endgroup$
    – user64494
    Feb 25, 2021 at 6:38
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    $\begingroup$ @user, I interpreted it as saying that the OP wants to see an explicit re-implementation of what Alpha does to compute a determinant step-by-step. $\endgroup$ Feb 25, 2021 at 6:47
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    $\begingroup$ Unfortunately, WolframAlpha["Det[RandomReal[{-1,1},{4,4}]]", {{"Result", 2}, "Content"}, PodStates -> {"Result__Step-by-step solution"}] performs "(step-by-step solution unavailable)". There is a room for an improvement in this direction. $\endgroup$
    – user64494
    Feb 25, 2021 at 7:00
  • $\begingroup$ @MarcoB: W|A says exactly the same. $\endgroup$
    – user64494
    Feb 25, 2021 at 13:27

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