If $\det(A) =3$ for some $n\times n$ matrix, what is $\det(A^{T} A)$? I know that $\det (A)=\det(A^T)$ but combined?
2026-03-26 17:35:34.1774546534
If detA =3 for some nxn matrix, what is det(A^T A)?
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$\newcommand{\mat}[1]{\mathbf{#1}}$ $$ \det (\mat A^\intercal \mat A) = \det \mat{A}^\intercal \det \mat A = (\det \mat A)^2 $$