Bias and variance calculation for Ridge estimator of β

Question

I understand how bias and variance for ridge estimator of β are calculated when the model is Y=Xβ + ϵ. But I have the model Y=X^tβ + ϵ. I don't understand if a model like that makes sense, can someone help me with that? If it does, how to derive the bias and variance for ridge estimator of β?

Thanks!