Show that AB = BA in each of the following cases:
(i) `A=[{:(costheta,-sintheta),(sintheta,costheta):}]" and "B=[{:(cosphi,-sinphi),(sinphi,cosphi):}]`
(ii) `A=[{:(1,2,1),(3,4,2),(1,3,2):}]" and "B=[{:(" "10,-4,-1),(-11," "5," "0),(" "9,-5," "1):}]`
(iii) `A=[{:(1,3,-1),(2,2,-1),(3,0,-1):}]" and "B=[{:(-2,3,-1),(-1,2,-1),(-6,9,-4):}]`

A=[[1,3,-12,2,-13,0,-1]] and B=[[-2,3,-1-1,2,-1-6,9,-4]]

IF A = [{:( -2,3,-1),( -1,2,-1),( -6,9,-4) :}] and B = [{:( 1,3,-1),( 2,2,-1),( 3,0,-1) :}] then

Verify that A(B+C)=(AB+AC), when (i) A=[{:(1,2),(3,4):}],B=[{:(2," "0),(1,-3):}]" and "C=[{:(1,-1),(0," "1):}]. (ii) A=[{:(2,3),(-1,4),(0,1):}],B=[{:(5,-3),(2," "1):}]" and "C=[{:(-1,2),(" "3,4):}].

if A=[{:(4,0,-3),(1,2,0):}]and B=[{:(2,1),(1,-2),(3,4):}]' then find AB and BA.

if A=[{:(1,2,3),(4,5,6):}]and B=[{:(-3,-2),(0,1),(-4,-5):}], then find AB and BA ,

Find AB and BA if exists from the following matrices A and B: (i) A=[{:(2,3,-1),(0,1,2):}]and B=[{:(2,-6),(-4,0):}] (ii) A=[{:(1,2,3),(0,1,-2),(-1,0,-1):}]and B=[{:(0,0,2),(2,0,0),(0,2,0):}] (iii) A=[{:(0,3,4),(2,1,-2),(1,-3,-1):}]and B=[{:(2,1,3),(-1,0,-2):}]

For each of the following pairs of matrices A and B, verify that (AB)'=(B'A'): (i) A=[{:(1,3),(2,4):}]" and "B=[{:(1,4),(2,5):}] (ii) A=[{:(3,-1),(-2,-2):}]" and "B=[{:(1,-3),(2,-1):}] A=[{:(-1),(2),(3):}]" and "B=[-2" "-1" "-4] (iv) A=[{:(-1," "2,-3),(4,-5," "6):}]" and "B=[{:(" "3,-4),(" "2," "1),(-1," "0):}]

If A=[{:(2,-1),(3,4),(1,5):}]" and "B=[{:(-1,3),(2,1):}] , find AB. Does BA exist?

Compute AB and BA, whichever exists when (i) A=[{:(2,-1),(3," "0),(-1," "4):}]" and "B=[{:(-2,3),(0,4):}] (ii) A=[{:(-1,1),(-2,2),(-3,3):}]" and "B=[{:(" "3,-2," "1),(" "0," "1," "2),(-3," "4,-5):}] (iii) A=[{:(0,1,-5),(2,4," "0):}]" and "B=[{:(1,3),(-1,0),(0,5):}] (iv) A=[1" "2" "3" "4]" and "B=[{:(1),(2),(3),(4):}] (v) A=[{:(2,1),(3,2),(-1,1):}]" and "B=[{:(1,0,1),(-1,2,1):}]

Given A=[{:(2,4,0),(3,9,6):}] "and" B=[{:(1,4),(2,8),(1,3):}] , is (AB)=B'A'?