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Automated proofs are a complicated subject. If you are not an expert on the subject, all you can hope for is to write a program where you can input a sample matrix (or that randomly generates one), and verifies the proposition for this particular case. If the proposition is confirmed in several cases, this makes the proposition plausible, but is by no means a formal proof.

Better try to prove it without writing any program.

Note: it is not even true; it is the inverse of the matrix which gives identity when is multiplied with the original matrix.

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Q: How can you write a program which proves that a multiple of a matrix and its determinant is an identity matrix?
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