Question

Find two square matrices A and B of order 2 such that AB=BA.​

Answer 1

Answer is (A+B)^2=(A-B)^2

Step-by-step explanation:

Given: A and B are square matrices

A^2=A,B^2=B,AB=BA=0

(A+B)^2=(A+B) (A+B)

(A+B)^2=A^2+AB+BA+B^2

=(A+B)^2=A+B (using given properties)

(AB)^2=(AB)(AB)=0

(A-B)^2=(A-B)(A-B)=0

(A-B)^2=A^2+B^2-AB-BA

=(A-B)^2=A+B (using given properties)

therefore (A+B)^2=(A-B)^2,

(AB)^2=0 and

(A-B)^2=A+B