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Consider the square matrices A and B, where B can be obtained from A by interchanging the rows of A. If det(A) is known, det(B) can be easily computed by counting the number of row interchanges. Each time a row is interchanged the sign of det(A) changes.
This videos shows two computational examples that demonstrate this matrix determinant property. This video does not PROVE this general result, it just demonstrates the property.
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