1. Solve the equation ab = cd for c, when a, b, c, d are numbers.
Solution: (ab)(1/d) = cd(1/d) = c, or c = ab/d.
2. Solve the equation ab = cd for d, when a, b, c, d are numbers.
Solution: (1/c)(ab) = (1/c)cd = d, or d = ab/c
NOTE: The notation ab/c only makes sense when multiplication is commutative and so (1/c)k = k(1/c) = k/c. NEVER use the notation with a "/" such as ab/c with transformations.
3. Solve the equation ab = cd for c, when a, b, c, d are transformations.
Solution: abd-1 = cdd-1 = c
4. Solve the equation ab = cd for d, when a, b, c, d are transformations.
Solution: c-1ab= c-1cd = d
5. Solve the equation ab = cd for c, when a, b, c, d are line reflections.
Solution: abd = cdd = c
6. Solve the equation ab = cd for d, when a, b, c, d are line reflections.
Solution: cab = ccd = d