Question

If A = `[(1,2),(3,-1)] , "B" = [(7,1),(2,5)]`

Verify that |AB| = |A|.|B|

Answer 1

AB = `[(1,2),(3,-1)] [(7,1),(2,5)] = [(7+4 , 1+10),(21-2 , 3 - 5)]`

∴ AB = `[(11,11),(19,-2)]`

|AB| = `|(11,11),(19,-2)|` = -22 - 209 = -231   ...(i)

|A| = `|(1,2),(3,-1)| = -1 - 6 = -7`

|B| = `|(7,1),(2,5)| = 35 - 2 = 33`

∴ |A| . |B| = - 7 × 33 = -231  ...(ii)

From (i) and (ii)

|AB| = |A|.|B|