Why does #(A+B)^2 = A^2+2AB+B^2# not work for matrices?
1 Answer
Feb 19, 2018
Because matrix multiplication is not generally commutative.
Explanation:
Matrix multiplication is associative and distributive over addition, but is not generally commutative.
So:
#(A+B)^2 = (A+B)(A+B) = A^2+AB+BA+B^2#
In general
#A^2+2AB+B^2#
For example:
#((1, 1), (0, 1))((0, 1),(1, 1)) = ((1, 2), (1, 1))#
#((0, 1),(1, 1))((1, 1), (0, 1)) = ((0, 1), (1, 2))#