# Math Help - proof involving inverses of invertible matrices

1. ## proof involving inverses of invertible matrices

Let A be an nxn invertible matrix.

I can't figure out how to prove the following:

t(A^-1) = (t(A))^-1. So the transpose of A inverse is equal to the inverse of A transpose.

2. So, if I understand, you wonder if equality $(A^{-1})^T=(A^T)^{-1}$ holds.

Multiply both sides by $A^T$: $(A^{-1})^TA^T=(A^T)^{-1}A^T$.
On the right-hand side of the equation you have identity matrix: $(A^{-1})^TA^T=I$.
And left-side, $(A^{-1})^TA^T$, equals identity matrix $(A(A^{-1}))^T=I$.

3. Ya, I just worked it out right before I checked your answer. Thanks anyways though.