If `A=[(1,3,-1),(2,2,-1),(3,0,-1)] and B=[(-2,3,-1),(-1,2,-1),(-6,9,-4)],` show that `AB=BA`

if A[{:(1,3,-1),(2,2,-1),(3,0,-1):}]and B=[{:(-2,3,-1),(-1,2,-1),(-6,9,-4):}], then show that AB=BA.

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):}]

If A={:[(0,1,2),(1,2,3),(3,1,1)]and B={:[(2,1,3),(-1,0,1),(3,-1,4)], show that, AB ne BA .

When are two matrices A and B said to be conformable for the product AB? If A={:((1,2,3),(1,3,3),(1,2,4))and B={:((6,-2,-3),(-1,1,0),(-1,0,1)) show that, AB = BA. Is it, in general, true for matrix multiplication? Give an example to justify your answer.

If A={:[(-2,1,3),(0,4,-1)]and B={:[(2,1),(-3,0),(4,-5)], show that, (AB)' = B'A' where A' is the transpose of A.

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

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

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.

If A={:[(2,0,9),(-1,6,10),(4,-1,2)]:},B={:[(0,-1,-2),(3,2,-1),(4,-2,0)]:} and C={:[(1,-2,0),(0,1,2),(3,0,-1)]:} then show that, A(B+C) = AB + AC.

If A={:[(2,0,9),(-1,6,10),(4,-1,2)]:},B={:[(0,-1,-2),(3,2,-1),(4,-2,0)]:} and C={:[(1,-2,0),(0,1,2),(3,0,-1)]:} then show that, A(BC) = (AB)C