Is the division of matrix is defined?
Or it is meaningless...
Many matrices do not have a matrix. Writing $\displaystyle AB^{-1}$ makes it clear that B must an inverse where $\displaystyle \frac{A}{B}$ does not.
Also, matrix multiplication is not, in general, commutative. Writing $\displaystyle \frac{A}{B}$ does not indicate whether $\displaystyle AB^{-1}$ or $\displaystyle B^{-1}A$ is intended.