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

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

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

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

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={:[(2,0,9),(-1,6,10),(4,-1,2)]:},B={:[(0,-1,-2),(3,2,-1),(4,-2,0)]:} and C={:[(1,-2,0),(0,1,2),(3,0,-1)]:} then show that, A(BC) = (AB)C

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)]

If a, b, c, d are in A.P. and a, b, c, d are in G.P., show that a^(2) - d^(2) = 3(b^(2) - ad) .

If A = [(a,b),(c,d)] show that, (i) adj (adj.A) = A (ii). (A^(-1))^(-1) = A .

If A=[{:(0,c,-b),(-c,0,a),(b,-a,0):}] and B=[{:(a^(2),ab,ac),(ab,b^(2),bc),(ac,bc,c^(2)):}] , then (A+B)^(2)= (a) A (b) B (c) I (d) A^(2)+B^(2)

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