1.Let $A \in GL_n(\mathbb{C})$. Show that $\det(I+A)=1+\operatorname{tr}(A)+ \epsilon(A)$ where Modulas of epsilon(A) by norm of A=0 as A tends to 0,for any matrix norm. If I define J(A)= det(A) for A is in GLn(C),then J is differentiable at all such A and that,if H is in Mn(C),then J'(A)(H)=det(A)tr(A*H). where A* is inverse of A.
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