If `A=((a, b), (c, d)) and I=((1, 0), (0, 1))` show that `A^(2)-(a+d)A=(bc-ad)I_(2).`

If a, b, c, d in R and A=[(a,b),(c,d)] , show that A^2-(a+d)A+(ad-bc)I is a null matrix.

If A=[(a,b),(c,d)],I=[(1,0),(0,1)] then A^(2)-(a+d)A=

(i) if A=[{:(1,0),(0,1):}],B=[{:(0,1),(1,0):}]and C=[{:(1,0),(0,1):}], then show that A^(2)=B^(2)=C^(2)=I_(2). (ii) if A=[{:(1,0),(1,1):}],B=[{:(2,0),(1,1):}]and C=[{:(-1,2),(3,1):}], then show that A(B+C)=AB+AC. (iii) if A=[{:(1,-1),(-1,1):}]and B=[{:(1,1),(1,1):}], then show that AB is a zero matrix.

(i) if A=[{:(1,0),(0,1):}],B=[{:(0,1),(1,0):}]and C=[{:(1,0),(0,1):}], then show that A^(2)=B^(2)=C^(2)=I_(2). (ii) if A=[{:(1,0),(1,1):}],B=[{:(2,0),(1,1):}]and C=[{:(-1,2),(3,1):}], then show that A(B+C)=AB+AC. (iii) if A=[{:(1,-1),(-1,1):}]and B=[{:(1,1),(1,1):}], then show that AB is a zero matrix.

A = [(1, 0), (0, 1)], B = [(1, 0), (0, -1)] and C = [(0, 1), (1, 0)] , then show that A^(2) = B^(2) = C^(2) = I^(2)

If A=[[a,b],[c,d]] and I=[[1,0],[0,1]] then A^2-(a+d)A-(bc-ad)I=

If A= [[a,b],[c,d]] and I= [[1,0],[0,1]] then A^(2)-(a+d)A=

if A = [(I,0)(0,-i)] then show that A^(2) = -1 (i^(2)=-1) .

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 .

If a, b, c and are real numbers and A =[{:( a,b),(c,d) :}] prove that A^(2) -(a+d) A+(ad-bc) I=0