If `A=[1 2 4 2]` , then show that `|2A|" "=" "4|A|`

If A=[1 2 3 3-2 1 4 2 1] , then show that A^3-23 A-401=0 .

If A=[[2,4],[-5,-1]] show that: |3A|=9|A|

If A=[3-3 4 2-3 4 0-1 1] , show that A^(-1)=A^3 .

(i) if A=[{:(1,-1),(2,3):}], then show that A^(2)-4A+5I=O. (ii) if f(x)=x^(2)+3x-5and A=[{:(2,-1),(4,3):}], then find f(A).

If |z-2|=2|z-1| , then show that |z|^(2)=(4)/(3)Re(z) .

If A=[{:(1,2,2),(2,1,2),(2,2,1):}] , then show that A^(2)-4A-5I_(3)=0 . Hemce find A^(-1) .

If A=[[2,-1],[-1, 2]] and I is the identity matrix of order 2, then show that A^2=4A-3I Hence find A^(-1) .

If A=[[1,-2, 3,],[ 4, 2, 5,]] and B=[[2, 4], [2,3],[ 5, 1]] , then find AB, BA. Show that A B!=B A .

.If A=[[1,4,7],[2,5,8]] and B=[[-3,4,0],[4,-2,-1]] then show that (A+B)^T=A^T+B^T

if A[{:(2,-3,-5),(-1,4,5),(1,-3,-4):}]and B=[{:(2,-2,-4),(-1,3,4),(1,-2,-3):}], then show that (i) AB=A and BA=B.