Suppose I am given a relation for 3x3 matrix $$AA^{T}=A^{T}A$$ and $$B=A^{-1}A^{T}$$ So what will be $B.B^{T}$ ? From first relation I concluded $A$ should be a symmetrical matrix and therefore $$B=A^{-1}A^{T}= A^{-1}A=I $$ therefore $B.B^{T}=I.I =I$ ($I$ is identity matrix) Is my logic correct ?
2026-04-09 15:18:53.1775747933
A doubt regarding symmetrical matrix
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$B.B^{T}=A^{-1}A^{T}.A{(A^{-1})}^{T}=A^{-1}AA^{T}(A^{T})^{-1}=I$