Advertisements
Advertisements
Question
If A = `[(3,7),(2,5)]` and B = `[(6,8),(7,9)]`, then verify that (AB)-1 = B-1A-1
Solution
Now AB = `[(3,7),(2,5)] [(6,8),(7,9)]`
`= [(18+49,24+63),(12+35,16+45)]`
`= [(67,87),(47,61)]`
|AB| = `= [(67,87),(47,61)]` = 4087 - 4089 = - 2
adj (AB) = `[(61,-87),(-47,67)]`
`("AB")^-1 = 1/|"AB"|` (adj AB)
`= 1/(-2) [(61,-87),(-47,67)]` ...(1)
Now we will find B-1A-1
B = `[(6,8),(7,9)]`, |B| = 54 - 56 = -2
adj B = `[(9,-8),(-7,6)]`
`"B"^-1 = 1/|"B"| ("adj B") = 1/(-2) [(9,-8),(-7,6)]`
A = `[(3,7),(2,5)]`, |A| = 15 - 14 = 1
adj A = `[(5,-7),(-2,3)]`
`"A"^-1 = 1/|"A"|` (adj A)
`= 1/1 [(5,-7),(-2,3)] = [(5,-7),(-2,3)]`
`"B"^-1"A"^-1 = 1/(-2)[(9,-8),(-7,6)][(5,-7),(-2,3)]`
`= 1/(-2)[(45+16,-63-24),(-35-12,49+18)]`
`= 1/(-2)[(61,-87),(-47,67)]` ......(2)
From (1) and (2),
(AB)-1 = B-1A-1
APPEARS IN
RELATED QUESTIONS
Find AB, if A = `((1,2,3),(1,-2,-3))` and B = `((1,-1),(1,2),(1,-2))`. Examine whether AB has inverse or not.
Choose the correct answer from the given alternatives in the following question:
If A = `[(lambda,1),(-1, -lambda)]`, and A-1 does not exist if λ = _______
Find the inverse of the following matrices by transformation method:
`[(2, 0, −1),(5, 1, 0),(0, 1, 3)]`
Choose the correct alternative.
If A is a 2 x 2 matrix such that A(adj. A) = `[(5, 0),(0, 5)]`, then |A| = _______
Check whether the following matrices are invertible or not:
`[(1, 2, 3),(2, 4, 5),(2, 4, 6)]`
A = `[(cos alpha, - sin alpha, 0),(sin alpha, cos alpha, 0),(0, 0, 1)]`, then A−1 is
If A = `[(1, 2),(3, -2),(-1, 0)]` and B = `[(1, 3, 2),(4, -1, 3)]` then find the order of AB
If A = `[(6, 5),(5, 6)]` and B = `[(11, 0),(0, 11)]` then find A'B'
The inverse of `[(1,cos alpha),(- cos alpha, -1)]` is ______.
A–1 exists if |A| = 0.
