Let A, B, C be matrices of order p × k, 3 × k and n × 3 respectively, then the conditions on n, k and p so that AB + CB will be defined are :

k = 3, p = n

A → p × k

B → 3 × k

C → n × 3

for AB & CB to be defined

for AB = k = 3

for CB = 3 = 3 (corresponding row and columns)

order (AB) = p × k

order (CB) = n × k

So AB + CD ⇒ order (AB) = order (CB)

so $p × k=n × k$

$⇒p=n$

so $k=3,p=n$