Yes! This should go without saying when referring to adults; when your child is an adult of course you should apologize to them and offer explanations same as you would any other adult.

I think where many mothers struggle with this in when dealing with little children and even tweens and teenagers. There’s so much that they just don’t know. How can we expect them to understand things unless we explain? How can we expect them to learn how to take responsibility for their actions and express remorse, unless we show them? No parent is perfect and when we do something wrong or that unintentionally hurts our child/children, of course we should apologize. This takes nothing away from you or hurts you in any way. What it does is show your child by example that even a mother can be wrong sometimes and even a child deserves to have that acknowledged, explained, and apologized for. When you have the maturity to apologize to your child, you help build their confidence and self-esteem.