Multiplying a determinant by a constant? book says

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SUMMARY

The determinant of a matrix multiplied by a constant is not simply the product of the determinant and the constant. For a 2x2 matrix A with a determinant of -5, the determinant of -3A is calculated as Det(-3A) = (-3)^2 * Det(A) = 9 * (-5) = -45. The confusion arises from the misunderstanding of how scalar multiplication affects the determinant, particularly in relation to the size of the matrix. This principle holds true for larger matrices as well.

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mr_coffee
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I'm confused, this question had 5 parts and i got the other 4 but this one I keep missing...
If A is a 2x2 matrix...
Det(A) = -5;
The Det(-3A);
The book said, if u multiply a column by a constant k then the determinant is also multiplied by k. So wouldn't the answer just be (-5)(-3) = 15?
Det(-3A) = 15? it says its wrong htough...:bugeye:
 
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Evaluate [tex]\left|\begin{array}{cc} ka& kb \\ kc&kd\end{array}\right|[/tex]... and compare it to [tex]\left|\begin{array}{cc} a& b \\ c&d\end{array}\right|[/tex]. Next try the 3x3 case.
 
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