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The determinant of a matrix is a useful tool for measuring how a linear transformation changes an area. In 3 dimensions, the determinant is also the volume of a parallelepiped that the cube turns into. The determinant is a natural way to describe orientation flipping, and it tells you how much a transformation scales things in 2 dimensions and 3 dimensions.

**00:00:00**The determinant is a useful tool for measuring how a linear transformation changes an area. It can be negative if the transformation inverts the orientation of space.**00:05:00**The determinant is a natural way to describe orientation flipping, and it tells you how much a transformation scales things in 2 dimensions and 3 dimensions. In 3 dimensions, the determinant is also the volume of a parallelepiped that the cube turns into. If both b and c are non-0, then the b * c term tells you how much the parallelepiped is stretched or squished in the diagonal direction.

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