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possible to solve this optimizationproblem with LMI?

hello guys, i got a problem like this. find the maximum of det(X), X=[x11,x12;x21,x22]. with the constraint x11^2+x21^2<1 und x12^2+x22^2<1. I think the constraint is not linear and it's not possible to use LMI to solve the problem. but i have not learnt LMI before. so i'd like to ask your opinions first. thx