The inverse of the matrix `[(1,0,0),(3,3,0),(5,2,-1)]` is

Options

A. `-1/3 [{:(-3,0,0),(3,1,0),(9,2,-3):}]`
B. `-1/3[{:(-3,0,0),(3,-1,0),(-9,-2,3):}]`
C. `-1/3 [{:(3,0,0),(3,-1,0),(-9,-2,3):}]`
D. `-1/3[{:(-3,0,0),(-3,-1,0),(-9,-2,3):}]`

Answer

B

Explanation

Let `A = |{:(1,0,0),(3,3,0),(5,2,-1):}|`
`rArr |A| = |{:(1,0,0),(3,3,0),(5,2,-1):}|`
`= 1 (3xx-1 - 0) - 0(3xx- 1- 0) + 0(3xx2- 5 xx3)`
`rArr |A| = 1 xx -3 - 0 -0 = -3"…"(i)`
Now, adj A
`=[{:(+(3xx-10),-(3xx-1-0),+(3xx2-5xx3)),(-(0-0),+(1xx-1-0),-(2xx1-5xx0)),(+(3xx0-0),-(1xx0-0),+(3xx1-0)):}]^(T)`
`= |{:(-3,3,6-15),(0,-1,-2),(0,0,3):}|^(T)`
adj `A = |{:(-3,0,0),(3,-1,0),(-9,2,3):}|^(T)"..."(ii)`
`:' A^(-1) = 1/(|A|)"adj" A = (1)/(-3)[{:(-3,0,0),(3,-1,0),(-9,-2,3):}]`
[from Eqs. (i) and (ii)]