Write the properties of determinant of matrix with an example for each.
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Properties of determinants
Interchange two rows or cols changes the sign: -> -1 * det(A) ...
transpose -> det (A) unchanged. ...
multiply row * k -> k * det(A) ...
multiply matrix * k -> k^2 * det(A) ...
det (A B) -> det(A) * det(B) ...
proportional rows or columns -> det() == 0. ...
Add multiple of one row to another -> det unchanged. ...
Geometric interpretation.
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