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,-3,22,0,-11,2,3]], then show that AA^(3)-4A^(2)-3A+11I=0 where O and I are null and identity matrix of order 3 respectively.

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, -2, 1),(0, 1 ,-1),(3, -1, 1)] then find A^(3)-3A^(2)-A-3I where I is unit matrix of order 3.

If A=([3,23,3]) and B=([1,-(2)/(3)-1,1]) show that AB=I_(2) where I_(2) is the unit matrix of order 2

If A is a non singular matrix and I is a unit matrix of order same as A such that A^(2)+A-I=O , then A^(-1) is equal to

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).

If A=[(1 ,0, 0),(0, 1,0),( a,b, -1)] , then A^2 is equal to (a) a null matrix (b) a unit matrix (c) A (d) A