Which of the following statements is/are true about square matrix A be order n ?  

${\left(A^T\right)}^{-1}={\left(A^{-1}\right)}^T$  holds always.

${(-A)}^{-1}$  is equal to $-A^{-1}$ where  n is odd only

If  A is skew-symmetric matrix of odd order, then its inverse exists.

If  $A^n=O,$ then  $I+A+A^2+\mathrm{.....}+A^{n-1}={(I-A)}^{-1}$