Given a square matrix \(A\) which of the following will always be true?
(I). \(A^TA=AA^T\)
(II). \(A-A^T\) is skew symmetric
(III). \(A^{-1}\) exists
(IV). \((A^T)^{-1}=(A^{-1})^T\)
1
I and IV only
2
II and IV only
3
II and III only
4
I and III only
Given a square matrix \(A\) which of the following will always be true?
(I). \(A^TA=AA^T\)
(II). \(A-A^T\) is skew symmetric
(III). \(A^{-1}\) exists
(IV). \((A^T)^{-1}=(A^{-1})^T\)