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A is m×n full rank matrix with m>n and 1 is an identity matrix. Let matrix A’ = (ATA)-1 AT. Then which one of the following statement is FALSE?
(a) AA’A = A (b) (AA’)2
(c) AA’A = 1 (d) AA’A = A’

1 Answer

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Given that $A'=(A^{T}A)^{-1}A^{T}$ 

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

Hence option (C) is false.

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