In matrix multiplication, does ABC=ACB if A, B, and C are nxn matrices?
1 Answer
Oct 24, 2015
In general, no.
Matrix multiplication is associative but not commutative.
Explanation:
Let
Then:
#ABC = BC = ((1, 1), (0, 0))((1, 0), (1, 0)) = ((2, 0), (0, 0))#
#ACB = CB = ((1, 0), (1, 0))((1, 1), (0, 0)) = ((1, 1), (1, 1))#
What is true for all
#(AB)C = A(BC)#
That is, matrix multiplication is associative.