If A=`[[1,-2,1],[0,1,-1],[3,-1,1]]`then find `A^(3)-3A^(2)-A-3I,` where I is unit matrix of order 3.

If A=[{:(,2,-1),(,-1, 3):}]" evaluate "A^2-3A+3I , where I is a unit matrix of order 2.

if A[{:(1,3,2),(2,0,3),(1,-1,1):}], then find A^(3)-2A^(2)+A-I_(3).

If A= [(1,1,3),(5,2,6),(-2,-1,-3)] then find A^(14)+3A-2I

If A=[{:(1,0,-1),(2,1,3),(0,1, 1):}] then verify that A^(2)+A=A(A+I) , where I is 3xx3 unit matrix.

If A=[[2,-1],[ 3, 2]] and B=[[0, 4],[-1, 7]] , find 3A^2-2B+I .

Let A=[(2,0,7),(0,1,0),(1,-2,1)] and B=[(-k,14k,7k),(0,1,0),(k,-4k,-2k)] . If AB=I , where I is an identity matrix of order 3, then the sum of all elements of matrix B is equal to

If A=[(1, 0,-3 ),(2, 1 ,3 ),(0, 1 ,1)] , then verify that A^2+A=A(A+I) , where I is the identity matrix.

show that [(1,1,3),(5,2,6),(-2,-1,-3)]=A is nilpotent matrix of order 3.

(A^(3))^(-1)=(A^(-1))^(3) , where A is a square matrix and |A|!=0

If A=[{:(,2,1,-1),(,0,1,-2):}] find: (i) A^(t).A (ii) A.A^(t) where A^t is the transpose of matrix A.