How do I manipulate my dataframe to keep the columns with matching rownames?

I have a data frame with 77 rows and 460 columns. The first column represents the rsID for each row titled "RS_number". The columns are each labeled by a SNP rsID (e.g., rs4751).

I need to limit this data frame to the dimensions 76 X 76, reflecting the same column names as the variable "RS_number". My first thought is to make the row.names equal to the first column "RS_number", but I am not sure how to move forward with this AND how to limit the columns to the same identifiers as the rownames.

Below is the code I used to create the data frame and a sample of the data frame:

'''newdf = concatenated[concatenated$RS_number %in% colnames(hours)[3:76],] %>% 
 as.data.frame()'''



     RS_number rs1 rs2 rs3 rs4 rs10
[,1]  rs1       1.0 0.2 0.3 0.4 NA
[,2]  rs2       0.0 1.0 0.0 NA  0.2
[,3]  rs3       0.2 0.1 1.0 NA  NA
[,4]  rs4       0.0 0.1 0.5 1.0 NA
[,5]  rs5       NA  0.1 NA  0.2 NA
[,6]  rs9       0.5 0.4 0.1 0.0 0.6

I would like my data frame to only keep those columns and RS_numbers that are common including rs1, rs2, rs3, rs4, and exclude rs5, and rs10.