Determinant of B is |B|=1.
Let $I$ be identity matrix.
1- Consider $A =CB$
$A$*$B^{-1}$=$C*B*B^{-1}$
$A*B^{-1}=C*I$ ($\because$ product of a matrix and it's inverse is identity matrix)
$\therefore C= A*B^{-1}$
since determinant of B is non zero,$B^{-1}$ exists.
Therefore, $A*B^{-1}$ exists.So we can say that there is a matrix C such that $A= CB$
2-
$A=BC$
$B^{-1}*A=B^{-1}*B*C$
$B^{-1}*A=I*C$ ($\because$ product of a matrix and it's inverse is identity matrix)
$C=B^{-1}*A$
since determinant of B is non zero,$B^{-1}$ exists.
Therefore, $B^{-1}*A$ exists.So we can say that there is a matrix C such that $A= BC$.
Therefore option A is true.