If matrix a has dimensions 1x3 and matrix b has dimensions 3x4, can these be multiplied?

A=1x3 means 1 row and 3 columns.
B=3x4 means 3 rows and 4 columns.

AB is a compatible multiplication because A has three columns and B has 3 rows.

However, BA is not a compatible multiplication because B has 4 columns while A has only 1 row.

The general trick is if you read the row/column of the two matrices as 1-3-3-4, and the two middle ones are identical, then AB would be a compatible multiplication.  On the other hand, BA would read 3-4-1-3, since 4 and 1 are not identical, so it is not a valid multiplication.

Do remember 1x3 means 1 ROW and 3 COLUMNS.