Could someone check this matrix calculation

Question

The first matrix dimension is 1 by 3
row 1 = 1
row 2 = 7
row 3 =3
Second matrix is 1 by 3
Row 1 column one =2
row 1 column two = -5
row one column three = 5
my calculation is that it would be the dimensions of 3 by 3
Final calcs would be row 1 column 1 = 2
row one-column two = -1
row one column three = 5
row two column 1 = 14
row two column two= -7
row two column three = 35
row three column one = 6
row three column two = -3
row three column three = 15

Is that correct?

Answer 1

when you describe the first matrix as
row 1 = 1
row 2 = 7
row 3 =3
you are describing a column matrix with dimension 3 by 1 , not 1 by 3

so I see you multiplying
1
7
3
by
2 -5 5

I got
2 -5 5
14 -35 35
6 -15 15

I am used to this notation :

m by n matix has m rows and n columns
Are you not using that same notation?

anyway, you could not multiply a 1by3 by a 1by3, no matter what notation you are used to