If `A=[(1, 2,-1),(-1, 1, 2),( 2,-1, 1)]`
, then `det(a d j\ (a d j\ A))`
is
`14^4`
(b) `14^3`
(c) `14^2`
(d) 14
Text Solution
Verified by Experts
We have, `A=[(1, 2,-1),(-1, 1, 2),( 2,-1, 1)]`
`∣A∣=1(1+2)−2(−1−4)−1(1−2)`
=`3+10+1=14`
We know that, for a square matrix of order n,
`adj(adjA)=∣A∣^(n−2)A, if ∣A∣!=0`
`det(adj(adjA))=∣∣A∣^(n−2)A∣
`
...
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=[(2,-1, 1),(-1, 2,-1),( 1,-1, 2)] , find (a d j A)^(-1) and (a d j A^(-1)) .
If A=[(2,3),(-1,4)] , find 4 A.
If A=[[1,-2,3],[0,-1,4],[-2,2,1]], then find |A| .
If A=[1 2 0-1 1 2 2-1 1],t h e ndet(A d j(A d jA))= 13 (b) 13^2 (c) 13^4 (d) None of these
If A=[[3,2],[1,4]], then A(adj A)=
If a d j\ A=[(2, 3),(4,-1)] and a d j\ B=[(1,-2),(-3, 1)] , find a d j\ A Bdot
For A[(3,1),(-1,2)] , then 14 A^(-1) is given by:
if A=[{:(3,-2),(7,1):}]and B=[{:(2,3),(-1,4):}], then find (i) A+B (ii) A-2B
For A=[(3,1),(-1,2)] then 14A^(-1) is given by :
If A=[{:(3,2),(1,4):}] , then what is A (adj A) equal to ?
