Home
Class 12
MATHS
Given A=[[5,0,4],[2,3,2],[1,2,1]] and B^...

Given `A=[[5,0,4],[2,3,2],[1,2,1]]` and `B^(-1)=[[1,3,3],[1,4,3],[1,3,4]]` . Compute `(A B)^(-1)` .

Text Solution

Verified by Experts

`A=[[5,0,4],[2,3,2],[1,2,1]]` and `B^(-1)=[[1,3,3],[1,4,3],[1,3,4]]`
`|A|=-1`
`adj A=[[-1, 8,-12],[0,1,-2],[1, -10, 15]]`
`A^(-1)=[[1, -8,12],[0,-1,2],[-1, 10, -15]]`
`(AB)^(-1)=B^(-1)A^(-1)`
`=[[1,3,3],[1,4,3],[1,3,4]] [[1, -8,12],[0,-1,2],[-1, 10, -15]]`
`=[[-2,19,-27],[-1,18,29],[-3,29,-42]]`
Promotional Banner

Topper's Solved these Questions

  • ADJOINTS AND INVERSE OF MATRIX

    RD SHARMA|Exercise QUESTION|1 Videos

  • ALGEBRA OF MATRICES

    RD SHARMA|Exercise Solved Examples And Exercises|410 Videos

Similar Questions

Explore conceptually related problems

If A=[[5,0,42,3,21,2,1]] and B^(-1)=[[1,2,31,4,31,3,4]]

Given A=[{:(5,0,4),(2,3,2),(1,2,1):}] , B^(-1)=[{:(1,2,3),(1,4,3),(1,3,4):}] . Compute (AB)^(-1) .

If A=[[1,2,3],[0,-1,4],[3,1,5]] and B=[[2,-1,0],[1,4,3],[3,0,-2]], verify that (AB)^-1=B^-1A^-1.

If A+B=[[1,2,1],[1,1,-1],[-3,2,4]] and A-B=[[-2,3,7],[-4,1,0],[2,4,1]] then 2A+4B equals

If A=[[0, 1,2],[1,2,3],[3,a,1]]and A^(-1)[[1//2,-1//2,1//2],[-4,3,b],[5//2,-3//2,1//2]] then

Given A=[[1,2,-3],[5,0,2],[1,-1,1]] and B=[[3,-1,2],[4,2,5],[2,0,3]] , find the matrix C such that A+C=B.

If A=[[2,3,-4],[1,0,6],[-2,1,5]],B=[[5,1,2],[6,-1,4],[5,3,-4]] , find 2A-3B .

If A=[[3,3,5],[4,4,4]] and B=[[1,3],[-1,2],[0,0]] then find AB

If A=[[1],[2],[3]]" and "B=[[-5,4,0],[0,2,-1],[1,-3,2]] , then find BA

If A = [[-1, 2 ,3],[-1, 0, 2],[1, -3, 1]] and B = [[4,5,6],[-1, 0, 1], [2,1,2]], find 4A-3B