If `A` satisfies the equation `x^3-5x^2+4x+lambda=0` , then `A^(-1)` exists if (a)`lambda!=1` (b) `lambda!=2` (c) `lambda!=-1` (d) `lambda!=0`

Options

A. `lambda ne 1`
B. `lambda ne 3`
C. `lambda ne-1`
D. `lambda ne 0`

Answer

D

Explanation

Since A satisfies the equation
`x^3-5x^2+4x+lambda=0`
`rArr A^3-5A^2+4A+lambdaI=0`
`rArr A(-A^2+5A-4I)=lambdaI`
`rArr A{1/lambda(-A^2+5A-4I)}=I," if " lambda ne 0`
Hence, `A^(-1)` exists and is equal to `1/lambda(-A^2+5A-4I)" if " lambda ne 0`.