How to proof that least square estimator $\hat{B}$ doesnt exist when $x$ is linearly dependent?

Question

For the linear regression model $Y=xB+e$, prove that if the columns of $X$ are linearly dependent, the least square estimator $\hat{B}$ does not exist

I know that since $\hat{B}$ is an unbiased estimator so X must be linearly independent , but how would i show that mathematically?

Answer 1

Hint:

The formula for the value of $\hat{B}=(X'X)^{-1}X'Y$ has an inverse in it, but not all matrices are invertible...