Normal Equation Roadblock

When solving linear regression via the closed-form normal equation $\beta = (X^\top X)^{-1} X^\top y$ , which condition makes this formula fail to produce a unique solution?

The features are not normalized to the same scale

$X^\top X$ is singular (not invertible), e.g. due to perfectly correlated features

The target variable y contains negative values

The number of training examples exceeds the number of features