Question

Can anyone prove y this identity wouldn't work for matrices

Answer 1

(a+b)(a+b)=a^2+2ab+b^2

Answer 2

This identity is true if and only if AB = BA. So you need just one example of a pair of matrices A and B where that is not the case.

Answer 3

Ok great thanks :D

Answer 4

problem is with the commutative law
\[(a+b)(a+b)=a^2+ab+ba+b^2\]and .. . what jamesj said

Answer 5

ok Good but I think I need to use an arguement

Answer 6

I have to show by example and arguement

Answer 7

Do i shld just say abt commutative law ok?

Answer 8

a counter example is all you need. it is almost never the case that
AB =BA

Answer 9

Alrighty Thanks :D

Answer 10

Write down a pair of 2x2 matrices and see if commute.

[
If you know anything about linear transformations, here are two that don't commute and you can see it geometrically:
- A = rotation pi/2 anti-clockwise
- B = reflection in the x-axis
]

Answer 11

Thanks