Question

A is m $\times$ n full rank matrix with m > n and I is an identity matrix. Let matrix A' = ($A^{T}A{)}^{-1}{A}^T$ , Then, which one of the following statement is TRUE?

• A. AA' A = A
• B. $(A{A}^{\prime }{)}^2=A$
• C. AA'A = I
• D. AA'A = A'

Answer 1

The correct option is A AA' A = A

A' = $(A^{T}A{)}^{-1}{A}^T$

AA' = $A{A}^{-1}(A^T{)}^{-1}{A}^T=I,I=I$

So AA'A = IA = A