Let `A=[(1,0,0),(0,1,1),(0,-2,4)],I=[(1,0,0),(0,1,0),(0,0,1)] and A^-1=[1/6(A^2+cA+dI)]` Then value of `c and d` are (a) `(-6,-11)` (b) `(6,11)` (c) `(-6,11)` (d) `(6,-11)`

Options

A. `(6, 11)`
B. `(6, -11)`
C. `(-6, 11)`
D. `(-6,-11)`

Answer

C

Explanation

Given, `A= [[1,0,0],[0,1,1],[0,-2,4]], A^(-1) = 1/6 [[6,0,0],[0,4,-1],[0,2,1]]`
`A^(2)= [[1,0,0],[0,1,1],[0,-2,4]] [[1,0,0],[0,1,1],[0,-2,4]]= [[1,0,0],[0,-1,5],[0,-10,14]]`
`cA= [[c,0,0],[0,c,c],[0,-2c,4c]] ,dI= [[d,0,0],[0,d,0],[0,0,d]]`
`therefore` By `A^(-1)=1/6[A^(2) + cA+dI]`
`rArr 6= 1 + c+d` [By equality of matrices]
`therefore (-6,11)` satisfy the relation.