# Matrix with elements in $L^\infty(0,T)$ means inverse matrix also has elements in $L^\infty(0,T)$?

Let $A(t)$ be a matrix with entries $a_{ij} \in L^\infty(0,T)$.

Suppose $A(t)^{-1}$ exists, and is positive-definite. Does it follow that $A(t)^{-1}$ has elements in $L^\infty(0,T)$ too?

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Consider the one-dimensional case... –  Anthony Carapetis Aug 30 '13 at 15:22