What is following product: diag(a₁,.., an)diag(b₁,.., bn)? When will: diag(a₁,.., an)diag(b₁...,bn) = I? Prove that diag(a₁,.., an) has an inverse provided none of its elements is zero. Consider square matrices A, B, X. Prove the following statements (assume the required inverses exist) (AB)-¹ = B-¹A-1 (X')-¹ = (x-¹)'

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