# Relation between determinant and matrix multiplication

I remember reading somewhere that if matrix multiplication can be done in $O(n^\omega)$ time then determinants can be computed in $O(n^\omega)$ time. I am unable to find the reduction and would it be possible for someone to share the reference?

• Try the book Algebraic Complexity Theory by Burgisser et al. – Yuval Filmus Feb 14 '16 at 6:16
• @YuvalFilmus I am also looking for 1 more piece of info. Group algebras and Matrix mult are related and matrix mult and determinants are related and so is there a relation between convolution in group algebras and determinant (and also permanent)? – user39969 Feb 14 '16 at 19:39