1. ## Proof

Not sure how to approach this one.

Prove $(A^{-1})^T = (A^T)^{-1}$.

2. that is equivalent to prove that

$({A}^{-1})^t \cdot {A}^t = I$

Owned by the transpose

$(A \cdot {A}^{-1})^t = I$

3. Originally Posted by kaylakutie
Not sure how to approach this one.

Prove $(A^{-1})^T = (A^T)^{-1}$.
Hi there,

$A^T (A^{-1})^T = (A^{-1})^T A^T = I$

Keeping in your mind the fact that $I^T = I$ you get

$A^T(A^{-1})^T = (A^{-1}A)^T = I ^T = I$

$(A^{-1})^T A^T = (AA^{-1})^T = I^T = I$