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    Proof about determinants

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    From Determinants.

    (From Determinants. Prove the proposition without using Cofactors/Cramer's rule.)

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    Solution Preview

    Please see the attachment.

    We should use the following properties of determinant.
    1. Switching two rows or columns changes the sign.
    2. Scalar multiplication of a row by a constant multiplies the determinant by .
    3. Multiplies of rows and columns ...

    Solution Summary

    This is a proof regarding determinants of elementary matrix and arbitrary square matrix.