Is A = I - X(X'X)⁻¹X' idempotent?

[BigDave48]

Let A= I - X(X'X)inverseX' to clarify: '=transpose; inverse of quantity (X'X)

1. Must A be a square matrix?
2. Must (X'X) be a square matrix?
3. Must X be a square matrix?
4. Show whether matrix A is an idempotent matrix (i.e. that AA=A)

Thanks.

 

[mathwonk]

im so stupid! i can't follow aNY OF THAT. if i could understand the question i could answer it instantly.

 

[BigDave48]

Sorry. I really would appreciate some help.

To be more clear: I is an identity matrix

Questions 1,2,and 3 are essentially Yes/No with a provided proof or explanation.

Does this help, clarify?

Thanks.

 

[mathwonk]

come on man.

 

[yenchin]

What do you mean by
"Let A= I - X(X'X)inverseX' to clarify: '=transpose; inverse of quantity (X'X)"

Sorry but it's incomprehensible.