Question

If A = `[(3, 2),(0, 5)] and "B" = [(1, 0),(1, 2)]` find the each of the following and state it they are equal: A² – B²  

Answer 1

Given
A = `[(3, 2),(0, 5)]`
and
B = `[(1, 0),(1, 2)]`
A² – B² 

= `[(3, 2),(0, 5)] xx [(3, 2),(0, 5)] - [(1, 0),(1, 2)] xx [(1, 0),(1, 2)]`

= `[(9 + 0, 6 + 10),(0 + 0, 0 + 25)] - [(1 + 0, 0 + 0),(1 + 2, 0 + 4)]`

= `[(9, 16),(0, 25)] - [(1, 0),(3, 4)]`

= `[(9 - 1, 16 - 0),(0 - 3, 25 - 4)]`

= `[(8, 16),(-3, 21)]`
We see that (A + B) (A – B) ≠ A² – B² .