# Kronecker Product

Is this right

$$\mathbf{A}\left(\mathbf{B}\otimes\mathbf{C}\right)\mathbf{D}=\left(\mathbf{A}\mathbf{B}\mathbf{D}\otimes\mathbf{C}\right)$$

No, that can't hold -- unless $C$ is $1\times 1$, the $A$ and $D$ matrices will need to have different dimensions for the two sides even to be defined.
For example, if $B$ and $C$ are both $2\times 2$ matrices, $B\otimes C$ will be a $4\times 4$ matrix, so $A(B\otimes C)D$ only makes sense if $A$ has 4 columns. But if that is true, then $ABD$ cannot exist, because $BD$ has only 2 rows, not 4.