Identify the true statements about the matrices

$A=\left[\begin{array}{ccc}1& 2& 4\\ 0& 1& 6\\ 5& 0& 1\end{array}\right],$ and $,B=\left[\begin{array}{ccc}1& -2& 8\\ 0& 1& -6\\ 7& 0& 1\end{array}\right]$

$BA=\left[\begin{array}{ccc}29& 0& 0\\ 42& 1& 0\\ 12& -10& 41\end{array}\right]$

$AB=\left[\begin{array}{ccc}41& 0& 0\\ -30& 1& 0\\ 12& 14& 29\end{array}\right]$

$AB=BA$

$BA=\left[\begin{array}{ccc}41& 0& 0\\ -30& 1& 0\\ 12& 14& 29\end{array}\right]$

$AB=\left[\begin{array}{ccc}29& 0& 0\\ 42& 1& 0\\ 12& -10& 41\end{array}\right]$

At least one of $AB$ or $BA$ do not exist.