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Is this right


Thanks in advance for your help.

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up vote 5 down vote accepted

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.

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