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**Question:**

The following are determinants of partial derivatives multiplied together giving another determinant of partial derivatives

Prove that this equality holds:

**Relevant Equations:**

|du/dx du/dy| |dx/dr dx/ds| |du/dr du/ds|

|dv/dx dv/dy| |dy/dr dy/ds| = |dv/dr dv/ds|

**Attempt at Solution:**

I took the determinant of first and second matrices, multiplied them together however the answer I got was twice the determinant that I expected. [ I expected to get: (du/dr)(dv/ds)-(du/ds)(dv/dr)]. Then when i tried to use the rule that the product of determinants is the determinant of products and took the determinant of the multiplied matrices i got four times the determinant that i expected.

Does this constant multiple matter or did I make a mistake. Pretty sure i got the algebra correct so is there an error in my reasoning?