You can check
https://www.familysearch.org/ for the marriage of Ernest J Matthews to Catherine A Lowe, 25 Feb 1920. It gives the names of her parents and his parents.
Looking at the census data:
1920 Fort Douglas, Salt Lake, Utah
Ernest J Mathews, 30, single, b. Idaho, parents b. Idaho, sergeant
U.S. Army
1910 South Boise, Ada, Idaho
Ernest Mathews, boarder, 20 single, b. Idaho, father b. MO, mo
mother b. Illinois, laborer, common laborer
1900 South Boise, Ada, Idaho
Edward J Matthews, b. Oct 1859, married 12 yrs, b. Missouri,
Ireland(?), Ohio, blacksmith
Eleanor wife, b. Mar 1858, married 12 yrs, mother of 7
children, 3 living, b. Iowa, Vermont, Indiana
Charles Spore, step-son, b. Sep 1877, b. Iowa, Illinois, Iowa
Ernest Matthews, son, b. Jan/Jun 1890
Looks like Edward J, the father, has married a Sophia by the 1910 census and is living in Coeur D'Alene, Kootenai, Idado. They have a 1 yr old daughter.