Originally Posted by: looseonthelead

Should the strings vibrate and make a sound when I lift my finger off A fret?

Yes, that happens. Sometimes it's unavoidable during certain motions, chord changes, or position shifts. But most of what you can do to avoid or at least lessen it that unwanted sound is learn to mute.

1. Mute with either or both hands when necessary. Watch this tutorial on various muting techniques.

https://www.guitartricks.com/tutorial.php?input=2281

2. Don't lift your fingers off the strings! When you need to change chords or notes, maintain light contact with the strings. Just release enough pressure that you stop the string from ringing & move into position for the next notes or chord. But always stay in contact with the string to mute unwanted sound.

Hope this helps!