SOCKS FIRST AND SHOES LATER

    Is it always A*B =B*A? yes.  4*3= 3*4.  It is elementary.  The multiplication said to obey "commutative law" in math.  It can be easily proved. Draw the dots as given below.

                                                     0  0  0
                                                     0  0  0
                                                     0  0  0
                                                     0  0  0

     It is 4*3 matrix -(4 rows and 3 columns).  Totally 12 dots.  Just rotate the page by 90 degrees.  We get 3*4 matrix.  But the total dots are 12 only.  Hence A*B=B*A.

     Say, you are shopping for a pair of jeans.  The price is 50 dollars.  But there is 20% discount.  And you have to pay 8% tax also.  A smart salesman may tell you "I will add the tax first and apply 20% discount on the total so that you will get more savings.
     Now we will do the calculation the salesman way,
              price 50 dollars
              8% of tax 4 dollars
              total     54  dollars
20% discount of 54 is 10.80
you have to pay 54-10.80 =43.20

     Let us find out what will happen if you apply the discount first.
20% discount of 50 is 10
price reduces to 50-10=40
8% tax on 40 is 3.20
Hence you have to pay 40+3.20 =43.20

    In both the cases, we arrive at the same figure.  Here, the commutative property of multiplication is in action.  So be smart.

    Commutative law is about the order of operations.  We will go for some real life examples.  You can wear left leg socks and right leg socks in any order.  But you cannot wear shoes first and socks later.  See the fun below.

  T + EA is not equal to EA+T
  Rubik cube rotations are not commutable.
    Now take two numbers 0 and 1.  First reverse them and then add.
0+1 reversed 1+0, adding get 1.
Next, first add and then reverse.
0+1 adding 1,  reversing 0
    It clearly illustrates that this order of operations are important in this case.

   In higher level physics called quantum mechanics says "If you measure the position of an atomic particle, its momentum will be disturbed.  Or if you measure momentum accurately first, then its position is disturbed".  That is, you cannot measure both accurately one after other.  This is the famous "uncertainty principle".

   A*B =B*A
   A+B = B+A
but
  A-B is not same as B-A
  A/B is not same as B/A
A simple property has so much content.
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