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

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

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

Let A = [(2,q),(0,1)] and A^(8) = [(x,yq),(0,1)], find x - y.

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

If A = [(1,-1,1),(2,-1,0),(1,0,0)] find A^(2) and show that A^(2) = A^(-1) .

If A={:[(2,-1),(3,2)]:} and B={:[(0,4),(-1,7)]:}, find 3A^(2)-2B+I

If A={:[(1,0),(1/2,1)]:} then A^(100)={:[(1,0),(10xxlamda,1)]:}, find the value of lamda .

If A={:[(1,2,1),(1,-1,1),(2,3,-1)]and B={:[(1,4,0),(-1,2,2),(0,0,2)], find the matrix AB - 2B.

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=[{:(1,0,0),(1,0,1),(0,1,0):}] , then which is true (a) A^(3)-A^(2)=A-I (b) det. (A^(100)-I)=0 (c) A^(200)=[(1,0,0),(100,1,0),(100,0,1)] (d) A^(100)=[(1,1,0),(50,1,0),(50,0,1)]