If `A=[1 2 2 2 1 2 2 2 1]` , then show that `A^2-4A-5I=O ,w h e r eIa n d0` are the unit matrix and the null matrix of order 3, respectively. Use this result to find `A^(-1)dot`

If A = ({:( 1,2,3),( 2,1,2),( 2,2,1) :}) and A^(2) -4A -5l =O where I and O are the unit matrix and the null matrix order 3 respectively if , 15A^(-1) =lambda |{:( -3,2,3),(2,-3,2),(2,2,-3):}| then the find the value of lambda

If A=[(2, 2),(9,4)] and A^(2)+aA+bI=O . Then a+2b is equal to (where, I is an identity matrix and O is a null matrix of order 2 respectively)

If A=[{:(1,2,2),(2,1,2),(2,2,1):}] , then show that A^(2)-4A-5I_(3)=0 . Hemce find A^(-1) .

If A=[{:(1,0,-1),(2,1,3),(0,1, 1):}] then verify that A^(2)+A=A(A+I) , where I is 3xx3 unit matrix.

Given [(4,2),(-1,1)] M = 6 I, where M is a matrix and I is the unit matrix or order 2xx2 . (ii) Find the matrix M.

If M=[{:(,4,1),(,-1,2):}] show that 6M-M^2=9I , where I is a 2 xx 2 unit matrix.

Matrix A such that A^2=2A-I ,w h e r eI is the identity matrix, the for ngeq2. A^n is equal to 2^(n-1)A-(n-1)l b. 2^(n-1)A-I c. n A-(n-1)l d. n A-I

Matrix A such that A^2=2A-I ,w h e r eI is the identity matrix, the for ngeq2. A^n is equal to 2^(n-1)A-(n-1)l b. 2^(n-1)A-I c. n A-(n-1)l d. n A-I

Given [(4,2),(-1,1)] M = 6 I, where M is a matrix and I is the unit matrix or order 2xx2 . (i) State the order of matrix M.

If A=[[2,-1],[-1, 2]] and I is the identity matrix of order 2, then show that A^2=4A-3I Hence find A^(-1) .