Let a $2 \times 2$ real matrix $A$ represent a reflection transformation of the coordinate plane and satisfy $A^{3} = \left[\begin{array}{cc} 0 & -1 \\ -1 & 0 \end{array}\right]$; let a $2 \times 2$ real matrix $B$ represent a rotation transformation (centered at the origin) of the coordinate plane and satisfy $B^{3} = \left[\begin{array}{cc} -1 & 0 \\ 0 & -1 \end{array}\right]$. Select the correct options. (1) There are exactly three possible matrices for $A$ (2) There are exactly three possible matrices for $B$ (3) $AB = BA$ (4) The $2 \times 2$ matrix $AB$ represents a rotation transformation of the coordinate plane (5) $BABA = \left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right]$
Let a $2 \times 2$ real matrix $A$ represent a reflection transformation of the coordinate plane and satisfy $A^{3} = \left[\begin{array}{cc} 0 & -1 \\ -1 & 0 \end{array}\right]$; let a $2 \times 2$ real matrix $B$ represent a rotation transformation (centered at the origin) of the coordinate plane and satisfy $B^{3} = \left[\begin{array}{cc} -1 & 0 \\ 0 & -1 \end{array}\right]$. Select the correct options.\\
(1) There are exactly three possible matrices for $A$\\
(2) There are exactly three possible matrices for $B$\\
(3) $AB = BA$\\
(4) The $2 \times 2$ matrix $AB$ represents a rotation transformation of the coordinate plane\\
(5) $BABA = \left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right]$