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If Det(A) is the change in volume, I would expect the sign to indicate whether the volume increased or decreased rather than the orientation. Can I get some more insight on why it doesn't tell me the increase/decrease of volume? wmarango

Can a given linear map only mirror once? If you mirror horizontally and then vertically, is this equivalent to no mirroring? The fact that the determinant can only either be positive or negative would suggest this. ScreenTime

How does it measure the change in volume? Could we go over it more in class? embl

What happens if the determinant is zero? (can there be a case?) willowpet

Does this mean the change in volume from a cube with dimensions (1,1,1)? ml2

How would this apply to structures that are difficult to represent with matrices? niyiqiul

Can we think of the matrix as implementation and determinant as an abstract concept? Zishen

if the direction changes along two dimensions, will the result still be positive? shoes

Why do we care about the change in volume and could we do a mathematical example about how the determinant tells the change in volume? anj

Not exactly familiar with how determinant describes a change in volume. How would we take the determinant in the above two cases to show that? Could we get examples? coolpotato

Do determinants represent anything for higher dimension matrices?