Home
Class 12
MATHS
if A=[{:(1,0),(0,1):}]and B=[{:(a,c),(b,...

`if A=[{:(1,0),(0,1):}]and B=[{:(a,c),(b,d):}],`then show that
`(AB)'=B'A'`

Text Solution

Verified by Experts

The correct Answer is:
N/a
`A.B=[{:(1,0),(0,1):}][{:(a,c),(b,d):}]`
`=[{:(a+0,c+0),(0+b,0+d):}]=[{:(a,c),(b,d):}]`
`implies (AB)=[{:(a,c),(b,d):}]'=[{:(a,c),(b,d):}]`
Again`A'=[{:(1,0),(0,1):}]'[{:(1,0),(0,1):}]`
`and B'=[{:(a,c),(b,d):}]=[{:(a,b),(c,d):}]`
`therefore B'A'=[{:(a,c),(c,d):}][{:(1,0)/(0,1):}]=[{:(a+0,0+b),(c+0,0+d):}]`
`=[{:(a,b),(c,d):}]=(AB)'.`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    NAGEEN PRAKASHAN|Exercise Exercise 3a|20 Videos

  • MATRICES

    NAGEEN PRAKASHAN|Exercise Exercise 3b|12 Videos

  • LINEAR PROGRAMMING

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|9 Videos

  • PROBABIILITY

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

If A=[{:(0,1),(1,1):}] "and" B=[{:(0,-1),(1,0):}] , then show that (A+B)(A-B)neA^(2)-B^(2)

(i) if A=[{:(1,0),(0,1):}],B=[{:(0,1),(1,0):}]and C=[{:(1,0),(0,1):}], then show that A^(2)=B^(2)=C^(2)=I_(2). (ii) if A=[{:(1,0),(1,1):}],B=[{:(2,0),(1,1):}]and C=[{:(-1,2),(3,1):}], then show that A(B+C)=AB+AC. (iii) if A=[{:(1,-1),(-1,1):}]and B=[{:(1,1),(1,1):}], then show that AB is a zero matrix.

if A=[(1,2),(3,4):}],B=[{:(-1,0),(2,3):}]and C=[{:(1,-1),(0,1):}], then show that : (i) A(B+C)=AB+AC (ii) (A-B)C=AC-BC.

if A=[{:(0),(1),(2):}]and B=[3" "2" "1], then show that : (AB)'=B'A'

If A=[(1,0),(0,3)] and B=[(2,0),(0,1)] then show AB =BA =[(2,0),(0,3)]

If A=[(1,0,),(2,0)] and B=[(0,0),(1,12)] then= (A) AB=0, BA=0 (B) AB=0,BA!=0 (C) AB!=0,BA=0 (D) AB!=0,BA!=)

If A=[{:(1,2),(-2,1):}],B=[{:(2,3),(3,-4):}] and C=[{:(1,0),(-1,0):}] , verfity (i) A(B+C)=AB+AC.

If A= [[2,4,-1],[-1,0,2]], B=[[3,4],[-1,2],[2,1]] , Show that (AB)'=B'A' .

If A=[[1,1] , [0,1]] and B=[[1,-1] , [0,1]] then AB=