# 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.

Proof:

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.

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