Let `A=[(1,-1,1),(2,1,-3),(1,1,1)]` and `10 B=[(4,2,2),(-5,0,alpha),(1,-2,3)]`.
If B is the inverse of A, then find the value `alpha`.

Options

A. 2
B. -1
C. 3
D. 5

Answer

D

Explanation

It is given that B is the inverse of matrix A.
`:. AB=I`
`rArr A(10B)=10I`
`rArr{:[(1,-1,1),(2,1,-3),(1,1,1)][(4,2,2),(-5,0,alpha),(1,-2,3)]=[(10,0,0),(0,10,0),(0,0,10)]:}`
`rArr{:[(10,0,5-alpha),(0,10,alpha-5),(0,0,alpha+5)]=[(10,0,0),(0,10,0),(0,0,10)]rArralpha=5:}`
ALITER : We have,
`AB=I`
`rArr A(10B)=10IrArr (A(10B))_13=0`
`rArr{:[(1,-1,1)][(2),(alpha),(3)]=0rArr 5-alpha=0rArr a=5:}`