Question

Let A = `|(3 , 2),(0 ,5)|` and B = `|(1 ,0),(1 ,2)|` , find (i) (A + B)(A - B)  (ii) A² - B² . Is (i) equal to (ii) ?

Answer 1

(i) A = `|(3 , 2),(0 ,5)|_(2 xx 2)` , B = `|(1 ,0),(1 ,2)|_(2 xx 2)` 

A + B = `|(3+1 , 2+0),(0+1 ,5 +2)| = |(4,2),(1,7)|_(2xx2)`

A - B = `|(3-1 , 2-0),(0-1 , 5-2)| = |(2 , 2),(-1,3)|_(2 xx 2)`

(A + B)(A - B) = `|(4 , 2),(1 , 7)|  |(2 , 2),(-1,3)|`

`=|(8 - 2 , 8+6),(2 - 7 , 2+21)| = |(6,14),(-5,23)|`  .......(1)

(ii)  A²

= `|(3,2),(0,5)| |(3,2),(0,5)| = |(9+0 , 6+10),(0 + 0 , 0+25)| = |(9,16),(0,25)|_(2 xx 2)`

 

B² = `|(1 ,0),(1 ,2)|  |(1 ,0),(1 ,2)| = |(1+0 , 0 + 0),(1 + 2 , 0 + 4)| = |(1 , 0),(3 , 4)|_(2 xx 2)`

 

A² - B² = `|(9,16),(0,25)| - |(1 , 0),(3 , 4)| = |(8,16),(-3 ,21)|_(2 xx 2)`       ..............(2)

from (1) and (2)

(i)  ≠  (ii)