Is (⟨A, B⟩)=trace(A B^T) an inner product in ℝ^n…

Is (⟨A, B⟩)=trace(A B^T) an inner product in ℝ^n ×m ? (The notation ⟨⟨A, B⟩⟩is chosen to distinguish this product from the one considered in Example 3 and Exer cise 4 .)

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