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

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=[(3,1),(-1,2)] , show that A^(2)-5A+7I=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={:((1,2),(-1,-2))and B={:((-1,3),(-3,1)). then show that, (A+B)^(2)ne A^(2)+2AB+B^(2).

If a=2^(1/3)-2^(-1/3) show that 2a^(3)+6a-3=0

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

If A = ((3,1),(-1,2)), I = ((1,0),(0,1)) and O = ((0,0),(0,0)) show that, A^(2) - 5A + 7I = O . Hence find A^(-1) .

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

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

If A=(1)/(2)(""_(1)^(0)" "_(0)^(1)),B=(1)/(2)(""_(i)^(0)" "_(0)^(-i)) and C=(""_(0)^(1)" "_(-1)^(0)) , show that, A^(2)+B^(2)+C^(2)=(3)/(2)I .