For two 3x3 matrices A and B, let A+B=2B' and 3A+2B=I3, where B' is the transpose of B and I3 is 3x3 identify matrix. Then :

A+B=2B' . (1)
Taking transpose on both sides, we have A'+B'=2B . (2)
3A+2B=I3 . (3)
Taking transpose on both sides, we get 3A'+2B'=I3 . (4)
Substituting equation (2) in (4), we have 3(2B-B')+2B'=I3
i.e.6B-B'=I3
Writing B'=A+B/2, we get 6B-A+B/2=I3
∴12B-A-B=2I3
i.e.11B-A=2I3
⇒11B-A=6A+4B
∴7B=7A
⇒A=B
Put this in equation (3)
⇒I3=3A+2A=5A=5B
⇒10A+5B=10A+5A=15A=3I3
Hence, option C is correct.