I have a class named ValidationsResult with this properties:

public class ValidationsResult
{
    public bool IsValid { get; set; }        

    public string[] Errors { get; set; }

    public void AddError(string error)
    {
        Errors.Append(error);
    }
}

But I want that the property IsValid to be read only, and depending if the object has Errors or not modify that property automatically.

How can I do that?

>Solution :

public class ValidationsResult
{
    public bool IsValid { get => Errors != null && Errors.Length == 0; }  // no errors = valid      

    public string[] Errors { get; set; }

    public void AddError(string error)
    {
        Errors.Append(error);
    }
}

That will make it readonly and it will tell you if you have errors

Based on the comment, yes. Better if you designed it in the following fashion.

public class ValidationsResult
{
    public bool IsValid { get => Errors.Count == 0; }  // or !Errors.Any()      

    public List<string> Errors { get; } = new List<string>();

    public void AddError(string error)
    {
        Errors.Add(error);
    }
}

You initialize the errors but outside consumer can still use it. Hence – next evolution

public class ValidationsResult
{
    private List<string> _errors  = new List<string>(); // private member

    public bool IsValid { get => _errors.Count == 0; }  // or !Errors.Any()      

    public string[] Errors { get => _errors.ToArray(); }

    public void AddError(string error)
    {
        _errors.Add(error);
    }
}

Now you encapsulating your error collection not letting consumer to modify it directly, but via AddError