Why Might the Square of a Sum Not Equal the Sum of Squares for Matrices?

[cmab]

(e+f)^2 = e^2+2ef+f^2
Why is this not neccesary true for squares matrices for all size?

 

[HallsofIvy]

(e+ f)^2= (e+f)(e+f)= e^2+ fe+ef+ fe. Remember that multiplication of matrices is not, in general, commutative!

 

[amcavoy]

(e+ f)^2= (e+f)(e+f)= e^2+ fe+ef+ fe. Remember that multiplication of matrices is not, in general, commutative!

Do you mean (e+f)² = e²+fe+ef+f²? I might be misinterpreting it but I can't see where that extra "fe" came from and where the "f²" went.

 

[AKG]

Yeah, that's what he meant: (e+f)² = e² + ef + fe + f².

 

[HallsofIvy]

One of these days, I'm going to learn to type!