To find the product ab of two matrices a and b, the number of in matrix a must equal the number of in matrix b.

A matrix A is identified as and matrix B is identified as .If the number of columns in A is the same as the number of rows in B, then you can multiply the matrices together.  The product matrix, then, is made up of what's left over:  rows from A and columns from B.  So your answers above are, in the first blank: columns, and in the second blank: rows.