Page 270 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

If we use column matrix notation for the vectors (7)
and omit the brackets on matrices, then it follows that
Thus, for vectors in column matrix notation, we have the following formula for the Euclidean inner product:
For example, if

then

If A is an matrix, then it follows from Formula 7 and properties of the transpose that (8)
The resulting formulas (9)

provide an important link between multiplication by an matrix A and multiplication by .
EXAMPLE 5 Verifying That
Suppose that
Then