I'm in an A+ course and was just working on wiring Ethernet cables. I was wondering, will an Ethernet cable function if the wires are reversed? Say instead of wiring 568B like striped orange, orange, striped green, blue, striped blue, green, striped brown, brown. Would it be possible for them to work when they're wired brown, striped brown, green, striped blue, and so on?
When you use TIA/EIA-568B on both sides this is a straight through cable. The colors of the inner jackets don't really matter, much the same as it makes no difference to the operation of the network if you use a network cable with a black or yellow outer jacket.
However, the standard is in place for a real reason, and that is that the cabling system should be implemented in a standard way so that anyone who works on it will intuitively understand what they are working on.
For instance, imagine if someone used your reversed wiring in a real environment, left, and you were now troubleshooting a cabling issue at that site. On inspection, you determine the cable is damaged and it need to be re-terminated on one side and did so with the standard TIA/EIA-568B. After doing so, the cable still will not work.
It isn't because your termination is bad, but because the cable is now a rolled cable. You may waste additional time/resources on trying to re-terminate the cable additional times. Unless you use a cable tester, you may not easily figure out that the cable is now a rolled cabled.
Ultimately, this potentially causes more problems/downtime and isn't really justifiable by any possible reason the original person may have had to not follow the standard.
Old answer (thinking the OP was talking about using TIA/EIA-568B on one side and the reverse on the other):
What you are describing is what is often referred to as a "rolled" or "rollover" cable. Pin 1 connects to pin 8 on the other side, pin 2 to pin 7, etc.
This type of cable would not work for network communications, but is used by many vendors for serial communication, such as console port access.
Simply addressing the connectivity of Ethernet cable, for short one as long as you use the same pairs at the same position it's OK.
For longer ones, you might have some crosstalk issue if you do it "however you want as long as it's the same pairs at both ends"
TIA/EIA-568A & B are only conventions to help everyone work together with less headache, there are no UTP-Police that will check your setup. Sure, they're supposed to be optimized (alternating signal/ground strands in the connector, centering Pair 1 to be able to use it for telephony if needs be, etc) but it's not like each pairs will refuse a signal if it's not at the right position in the connector. Also, if you follow the standard, it's quite easy to differentiate Straight/Roll-Over/Cross-Over cables.
It's the same thing as the Jacket color (In UTP structured cabling. Fiber jacket color actually means something). Even if the cables are Blue, Red, White or Black, they're still an Ethernet Cable (barring rolled-over or crossed-over ones), meaning you can use whichever colors you like, but it's still a good idea to be able to see their function by using different colors (as long as you stick to it!)