If `A={:((1,4),(2,3)),` show that, `A^(2)-4A-5I=0` where `I={:((1,0),(0,1))and 0={:((0,0),(0,0)).`

If A=({:(1,4),(2,3):}) , then show that A^(2)-4A-5I=0 ,where I=({:(1,0),(0,1):}) " and " O=({:(0,0),(0,0):}) .

If A=[(3,1),(-1,2)] , show that A^(2)-5A+7I=0 .

If A={:((1,2),(-3,0)), show that, A^(2)+3A+5I={:((3,8),(-12,-1)).

If A = [[3,-5],[-4,2]] ,show that A^2 -5A-14I =0.

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

If A=({:(2,-1),(1,3):}) , then show that A^2-5A+7I_2=0 : hence find A^(-1) .

Verify that the matrix equation A^(2)-4A+3I = 0 is satisfied by the matrix A={:[(2,-1),(-1,2)]," where " I={:[(1,0),(0,1)]and 0={:[(0,0),(0,0)]. Hence obtain A^(-1).

If A=([2,-1],[1,3]) then show that A^2-5A+7I_2=0 hence find A^(-1)

If A={:((4,2),(-1,1))and I={:((1,0),(0,1)), prove that, (A-2I)(A-3I)={:((0,0),(0,0)).

If A =[{:(2,0,0),(0,3,0),(0,0,5):}] , prove that, A^(2)=[{:(2^(2),0,0),(0,3^(2),0),(0,0,5^(2)):}] , hence by induction method show that, A^(n)=[{:(2^(n),0,0),(0,3^(n),0),(0,0,5^(n)):}]