Home
Class 12
MATHS
Show tha, A={:[(1,2,2),(2,1,2),(2,2,1)]:...

Show tha, `A={:[(1,2,2),(2,1,2),(2,2,1)]:}` satisfies the equation `A^(2)-4A-5I_(3)=0.` Hence find `A^(-1).`

Text Solution

Verified by Experts

The correct Answer is:
`1/5{:[(-3,2,2),(2,-3,2),(2,2,-3)]:}`
Promotional Banner

Similar Questions

Explore conceptually related problems

Show that, the matrix A = [(1,2,2),(2,1,2),(2,2,1)] satisfies the equation A^(2) - 4A - 5I_(3) = 0 and hence find A^(-1) .

Show that A = [[1,2,2],[2,1,2],[2,2,1]] satrisfies the matrix equation A^2-4A-5I_3 =0

Show that the matrix A=[[1,2,2],[2,1,2],[2,2,1]] satisfies the equation A^2-4A-5I_3=O and hence find A^(-1)

Show that the matrix A=({:(2,-3),(3,4):}) satisfies the equation A^(2)-6A+17I=O and hence find A^(-1) where I is the identity matrix and O is the null matrix of order 2 times 2 .

Show that the matrix A= [(2,-3),(3,4)] satisfies the equation x^(2) - 6x + 17 = 0. Hence find A^(-1)

If A=(1)/(3){:[(-1,2,-2),(-2,1,2),(2,2,1)] show that "AA"^(T)=I .

If the matrix A = [(1,2),(3,4)] satisfies the equation A^(2) = 5A + 2I . Then, find the value of A^-1 .

A={:[( 1,1,1),(1,2,-3),(2,-1,3)]:} Show that A^(3) - 6A^(2) +5A +11 I =O. Hence , find A^(-1)

If A=1/3({:(-1,2,-2),(-2,1,2),(2,2,1):}) , show that "AA"^(T)=I_(3) .

If A=[(1,2,3),(3,-2,1),(4,2,1)] , then show that A^(3)-23A-40I=0