If `A=[(1,-1),(-1,1)] and B=[(1,1),(1,1)],` prove that `AB` is null matrix.

If A=[(1, -1), (-1, 1)] and B=[(1, 1), (1, 1)] then 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=[(1,2),(3,-1)]" and B "=[(1,3),(-1,1)] , then matrix AB is a :

If A=[(1,0),(0,-1)] and B=[(0,1),(1,0)] . Find AB and BA. Prove that AB ne BA .

If A = {:[(1,2),(0,1)], B = [(1,-3),(2,4)] and C = [(1,-1),(-1,2)] then prove that : (AB)' = B'A'

If A = [(7,8),(1,9)] and B = [(7,12),(5,1)] , find the matrix C such that 3 A + 5 B + 2 C is a null matrix.

If A = [(9, 1),(7,8)] and B = [(1,5),(7,12)] , find the matrix C such that 5 A + 3 B + 2 C is a null matrix.

If A = {:[(1,2),(0,1)], B = [(1,-3),(2,4)] and C = [(1,-1),(-1,2)] then prove that : A(B+C) = AB+AC