Consider matrices $A,B,C$ and $D,$ where $A$ is $23,B$ is $33,C$ is $42$ and $D$ is $34.$ Which statement is true?

$($A$)AB+CD$ is defined, and its dimension is $23.$

$($B$)CA+BD$ is defined, and its dimension is $43.$

$($C$)$ ABD is defined, and its dimension is $23.$

$($D$)$ BDA is defined, and its dimension is $34.$

$($E$)$ DCA is defined, and its dimension is $33.$

$($F$)$ None of the above is true.