0 votes 0 votes 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’ Linear Algebra linear-algebra matrix + – Prince Sindhiya asked Mar 2, 2018 retagged May 6, 2021 by Shiva Sagar Rao Prince Sindhiya 2.2k views answer comment Share Follow See 1 comment See all 1 1 comment reply pilluverma123 commented Mar 3, 2018 reply Follow Share Please upload the photo of the question. 0 votes 0 votes Please log in or register to add a comment.
1 votes 1 votes 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. Abhisek Das answered Mar 3, 2018 edited Mar 3, 2018 by Abhisek Das Abhisek Das comment Share Follow See all 2 Comments See all 2 2 Comments reply lolster commented May 30, 2019 reply Follow Share Since A is not a square matrix, we cannot write $(A^{T}A)^{-1} = A^{-1}(A^{T})^{-1}$ simply because they individually do not exist. 0 votes 0 votes SURYA TEJA 1 commented Nov 27, 2019 reply Follow Share Option 4 is also false we can't even compare LHS and RHS as orders are different. 0 votes 0 votes Please log in or register to add a comment.