Not sure how to approach this one. Prove $\displaystyle (A^{-1})^T = (A^T)^{-1}$.
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that is equivalent to prove that $\displaystyle ({A}^{-1})^t \cdot {A}^t = I$ Owned by the transpose $\displaystyle (A \cdot {A}^{-1})^t = I$
Originally Posted by kaylakutie Not sure how to approach this one. Prove $\displaystyle (A^{-1})^T = (A^T)^{-1}$. Hi there, $\displaystyle A^T (A^{-1})^T = (A^{-1})^T A^T = I$ Keeping in your mind the fact that $\displaystyle I^T = I$ you get $\displaystyle A^T(A^{-1})^T = (A^{-1}A)^T = I ^T = I$ $\displaystyle (A^{-1})^T A^T = (AA^{-1})^T = I^T = I$ This completes your proof.
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