If `A=({:(1,2),(2,3):})and B=({:(1,0),(1,0):})` then what is determinant of AB ?

If A = ((1,2),(2,3))and = ((1,0),(1,0)) , then what is the value of determinant of AB ?

If A=[(2,3),(1,2)], B = [(1,0),(3,1)] then what is determinant of AB

(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.

IF A=[{:(2,-1,2),(1,3,-4):}] and B=[{:(1,-2),(-3,0),(5,4):}] then verify that (AB)'=B'A'.

(i) if A=[{:(1,-4),(3,1):}]and b=[{:(1,0,5),(-2,4,3):}], then show that : (AB)'=B'A' (ii) if A=[{:(2,3),(0,1):}]and B=[{:(3,4),(2,1):}], then prove that : (AB)'=B'A'

if A=[{:(4,3,2),(-1,2,0):}], B=[{:(1,2),(-1,0),(1,-2):}] then |AB| = ……..

If A=[{:(1,2),(-2,1):}],B=[{:(2,3),(3,-4):}] and C=[{:(1,0),(-1,0):}] , verfity (i) A(B+C)=AB+AC.