Home
Class 12
MATHS
If A is non-singular and (A-2I)(A-4I)=0 ...

If `A` is non-singular and `(A-2I)(A-4I)=0 , then ,1/6A+4/3A^(-1)` is equal to

A

`O`

B

`I`

C

`2I`

D

`6I`

Text Solution

Verified by Experts

The correct Answer is:
B
we have, `(A-2I) (A-4I) = 0`
`rArr A^(2) - 4A - 2 A + 8 I^(2) = 0`
`rArr A^(2) - 6 A+ 8 I =0`
`rArr A^(-1) (A^(2)-6A=8I) = A^(-1)0`
` rArr A- 6 I + 8 A^(-1) = 0`
`rArr 1/6 A + 4/3 A^(-1) = I`
Promotional Banner

Similar Questions

Explore conceptually related problems

If A is a 3xx3 non - singular matrix and if |A| = 3 , then | (2A)^(-1)| =

If A^(2) - 3 A + 2I = 0, then A is equal to

If A is 3xx 3 non- singular matrix and if |A |=3 then |(2A)^(-1) |=

If A is a 3xx3 non -singular matrix , then det . [ adj .A] is equal to :

If A=[(1,-3),(2,k)] and A^(2)-4A+10I=A , then k =

If S is a real skew-symmetric matrix, then prove that I-S is non-singular and the matrix A=(I+S)(I-S)^(-1) is orthogonal.

If n is an odd integer, then (1+i)^(6 n)+(1-i)^(6 n) is equal to

If A^5=0 such that A^n != I for 1 <= n <= 4 , then (I - A)^-1 is equal to

If A = [(i,0),(0,i)] then A^(4n) (n in N ) equals :