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