let A be a 5 X 3 matrix and B be a 3 X 5 matrix
a) is it possible to add A and B?
No, because in order to add them, they must have exactly
the same dimensions.
b) is it possible to do the multiplication AB?
Yes because there are the same number of columns in the
first matrix A, 5 x 3, as there are columns in B, the
3 x 5 matrix. That is when you write their dimensions
in the order you are wanting to multiply them:
5 x 3 times 3 x 5
The inner dimensions are both the same, in this case 3.
And their product will be a 5 x 5, the outer two
dimensions.
c) is it possible to do the multipllication BA?
Yes because there are the same number of columns in the
first matrix B, 3 x 5, as there are columns in A, the
5 x 3 matrix. That is when you write their dimensions
in the order you are wanting to multiply them:
3 x 5 times 5 x 3
the inner dimensions are both the same, in this case 5.
And their product will be a 3 x 3, the outer two
dimensions.
Edwin
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