$\"\"$

First find the matrix product C(A+B)

$\"\"$

First find the matrix product AC

$\"\"$

Multiply columns by rows.

$\"\"$

Find the products BC.

$\"\"$

Multiply columns by rows.

$\"\"$

Add AC and BC

Multiply columns by rows.

$\"\"$ + $\"\"$

$\"\"$

The solution of equation C(A + B)= AC+BC is False.