If `I={:((1,0),(0,1)):}` and `E={:((0,1),(0,0)):}` prove that, `(2I+3E)^(3)=8I+36E.`

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

If A={:[(0,-1),(1,0)]:} and B={:[(0,i),(i,0)]:} , then

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={:[(a,b),(c,d)] and I={:[(1,0),(0,1)] Show that, A^(2)-(a+d)A=(bc-ad)I .

If A={:[(1,0),(-1,7)] and I={:[(1,0),(0,1)] , then find k so that A^(2)=8A+kI

Let, I=({:(1,0,0),(0,1,0),(0,0,1):}) " and " P=({:(1,0,0),(0,-1,0),(0,0,-2):}) . Then the matrix P^(3)+2P^(2) is equal to -

If A={:[(1,2,x),(0,1,0),(0,0,1)]:}, B={:[(1,-2,y),(0,1,0),(0,0,1)]:} and AB=I_(3) , then find the value of x + y + 1.

If A=[(1,0,2),(0,2,1),(2,0,3)] , prove that A^(3)-6A^(2)+7A+2I=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):}) .

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).