SOLUTION: If A and B are n×n matrices, then (A + B)(A – B) = A^2 – B^2.

Algebra.Com
Question 1101239: If A and B are n×n matrices, then (A + B)(A – B) = A^2 – B^2.
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!

That's false.  Here's a counter-example:









  <--this does not equal to





  <-- this

So as you see, 

They are not equal.

Edwin

RELATED QUESTIONS

On what condition the property holds in matrices {{{ A^2 - B^2}}} = (A - B).(A + B) where (answered by ikleyn)
Q−1: [5×2 marks] Answer each of the following as True or False justifying your... (answered by math_tutor2020)
Suppose A and B are nxn matrices. Which of the following statements is true? 1. If B is... (answered by jsmallt9)
if a^n = b^n, then is a=b,... (answered by richwmiller)
If n(A) = 14, n(A union B) = 17, and n(B) = 9, then what is n(A ∩ B)? (answered by MathLover1)
If n(A) = 5, n(A ∪ B) = 8, and n(B) = 5, then what is n(A ∩... (answered by MathLover1)
Given two n x n matrices A and B where AB=BA how does one show that the determinant of... (answered by khwang)
If A and B are disjoint sets then n(AUB)=n(A)+n(B). Verify with the help of... (answered by sachi)
if n < m and a < b, then a. n+a > m+b b. m=b c. n=a d. n+a <... (answered by tommyt3rd)