If they were ok before you rotated them, then they should be ok after you rotate them, except for really small numerical errors. These errors are only a problem if you keep applying rotations to a matrix frame after frame, instead of rebuilding it from scratch each time, so most of the time this isn't required.
If it is required, you can use the cross product to find a vector that's perpendicular to two others. Pick 2 of your vectors and cross them to regenerate the 3rd. Then use the 1st and the 3rd to regenerate the 2nd. Each time you regenerate one, you can check it's dot product with the original version; it should be very close to 1.0 or -1.0. If it's negative, then flip the regenerated vector so it matches the direction/handedness of the original.