# Let M and N be matrices , #M = [(a, b),(c,d)] and N =[(e, f),(g, h)],# and #v# a vector #v = [(x), (y)].# Show that #M(Nv) = (MN)v#?

##### 1 Answer

Aug 4, 2016

This is called an *associative law* of multiplication.

See the proof below.

#### Explanation:

(1)

(2)

(3)

(4)

Notice that the final expression for vector in (2) is the same as the final expression for vector in (4), just the order of summation is changed.

End of proof.