Find number of elements in `{A=[(a,b),(0,d)] , a,b,d in{-1,0,1}` such that `{(I-A)^3=I-A^3} I is 2 xx2` identity matrix

The number of elements in the set {A = ((a, b),(0, d)): a, b, d in {-1, 0, 1) " and " (I - A)^(3) = I - A^(3)} , where I is 2 xx 2 identity matrix, is ___________.

If A=[[1,0,-32,1,30,1,1]], then verify that A^(2)+A=A(A+I), where I is the identity matrix.

Consider a matrix A=[(0,1,2),(0,-3,0),(1,1,1)]. If 6A^(-1)=aA^(2)+bA+cI , where a, b, c in and I is an identity matrix, then a+2b+3c is equal to

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

Let A = [(1,1,0),(0,1,0),(0,0,1)] and let I denote the 3xx3 identity matrix . Then 2A^(2) -A^(3) =

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

If A is a square matrix and |A|!=0 and A^(2)-7A+I=0 ,then A^(-1) is equal to (I is identity matrix)

If A = [(3,1),(5,2)] , and AB = BA = I, then find the matrix B.

Let A and B are two non - singular matrices of order 3 such that A+B=2I and A^(-1)+B^(-1)=3I , then AB is equal to (where, I is the identity matrix of order 3)