For the OLS estimator = ( X)-1 Y to exist,X'X must be invertible.This is the case when X has full rank.What is the rank of a matrix? What is the rank of the product of two matrices? Is it possible that X could have rank n? What would be the rank of X'X in the case n

Question

For the OLS estimator  = (  X)-1  Y to exist,X'X must be invertible.This is the case when X has full rank.What is the rank of a matrix? What is the rank of the product of two matrices? Is it possible that X could have rank n? What would be the rank of X'X in the case n<(k+1)? Explain intuitively why the OLS estimator does not exist in that situation.

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The Answer of For the OLS estimator  = (  X)-1  Y to exist,X'X must be invertible.This is the case when X has full rank.What is the rank of a matrix? What is the rank of the product of two matrices? Is it possible that X could have rank n? What would be the rank of X'X in the case n<(k+1)? Explain intuitively why the OLS estimator does not exist in that situation.

For the OLS Estimator = ( X)-1