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?