If `A=[4-1-4 3 0-4 3-1-3]` , show that `A^2=I_3dot`

If A=[4-1-430-43-1-3], show that A^(2)=I_(3)

(i) if A=[{:(4,-1,-4),(3,0,-4),(3,-1,-3):}], then show that A^(2)=I

If A=[2-3-5-1 4 5 1-3-4] and B=[2-2-4-1 3 4 1-2-3] , show that A B=A and B A=B .

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=[(4,2),(-1,1)] , show that (A-2 I) A-3 I) =0

If A=|{:(4,-1,-4),(3,0,-4),(3,-1,-3):}| , then show that A=A^(-1)

If A=[{:(2,-2,-4),(-1," "3," "4),(1,-2,-3):}], show that A^(2)=A.

If A=[[1,2,1] , [1,-4,1] , [3,0,-3]], B=[[2,1,1] , [1,-1,0] , [2,1,-1]] then show that AB=6I_3

(i) if A=[{:(1,-1),(2,3):}], then show that A^(2)-4A+5I=O. (ii) if f(x)=x^(2)+3x-5and A=[{:(2,-1),(4,3):}], then find f(A).

If A=[(1, 2, 0 ),(3,-4, 5),( 0,-1, 3)] , compute A^2-4A+3I_3 .