Matrix differentiation and inverse: How can I prove det(∂/∂A tr(A^-1))≠0 ?

Asangi_a4ac

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Matrix differentiation and inverse: How can I prove det(∂/∂A tr(A^-1))≠0 ?

How can I prove det(∂/∂A tr(A^-1))≠0 ?
 
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