Arulmigu Siddhi Buddhi Vinayagar - History
The Ganesha Purana and the Mudgala Purana contain descriptions of Ganesha flanked by Siddhi and Buddhi. In these two Puranas they appear as an intrinsic part of Ganapati and according to Thapan do not require any special rituals associated with shakti worship. In Chapter I.18.24-39 of the Ganesha Purana, Brahmā performs worship in honor of Ganesha, and during it Ganesha himself causes Buddhi and Siddhi to appear so that Brahmā can offer them back to Ganesha. Ganesha accepts them as offerings. In Ganesha Purana I.65.10-12 there is a variant of this incident, in which various gods are giving presents to Ganesha, but in this case Siddhi and Buddhi are born from Brahmā's mind and are given by Brahmā to Ganesha.
The Ganesha Temple at Morgaon is the central shrine for the regional aṣṭavināyaka complex. The most sacred area within the Moragaon temple is the sanctum (garbhagŗha), a small enclosure containing an image of Ganesha. To the right and left sides of the image stand Siddhi and Buddhi. In northern India the two female figures are said to be Siddhi and Riddhi. There is no evidence for the pair, but the pairing parallels those of Buddhi and Siddhi in Shiva Purana and Riddhi and Buddhi from Matsya Purana.
Hence Brahma Saraswati Become Ganesha's Father in Law and Mother in Law.
As Ganesha had an elephant-head no girl was ready to marry him. While all other gods had a consort he did not have one and this angered Ganesha. He started creating problems in the marriages of Devas (demigods). He asked rats to dig up holes on the path through which wedding procession of any Deva would go to the bride’s house. The Devas faced innumerable problems in their weddings. Fed up with the activities of Ganesha, the Devas complained to Brahma, who agreed to solve the problem. To please Ganesha, Brahma(Prajapati)created two beautiful women named Riddhi (wealth and prosperity) and Siddhi (intellectual and spiritual powers). Brahma gave them in marriage to Ganesha.From that day onwards whoever pleases Ganesha also gets the blessings of Siddhi and Riddhi.