Transpose Of A Matrix

M%3D%5Cbegin%7Bbmatrix%7Dx%20%26%20x%20%5C%5C%20x%20%26%20x%5Cend%7Bbmatrix%7D%2C%20%5Cforall%20x%20%5Cin%20R

and

x%20%5Cneq%200

Let

P

be the identity element in the group
i.e.

P%3D%5Cbegin%7Bbmatrix%7D%5Cfrac%7B1%7D%7B2%7D%20%26%20%5Cfrac%7B1%7D%7B2%7D%20%5C%5C%20%5Cfrac%7B1%7D%7B2%7D%20%26%20%5Cfrac%7B1%7D%7B2%7D%5Cend%7Bbmatrix%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Cbegin%7Bbmatrix%7D1%20%26%201%20%5C%5C%201%20%26%201%5Cend%7Bbmatrix%7D

P

is obtained by putting

x%3D%5Cfrac%7B1%7D%7B2%7D

%5Ctherefore%20%5C%2C%20M%20P%3D%5Cbegin%7Bbmatrix%7Dx%20%26%20x%20%5C%5C%20x%20%26%20x%5Cend%7Bbmatrix%7D%5Cbegin%7Bbmatrix%7D%5Cfrac%7B1%7D%7B2%7D%20%26%20%5Cfrac%7B1%7D%7B2%7D%20%5C%5C%20%5Cfrac%7B1%7D%7B2%7D%20%26%20%5Cfrac%7B1%7D%7B2%7D%5Cend%7Bbmatrix%7D%3DM

and

PM%3D%5Cbegin%7Bbmatrix%7D%5Cfrac%7B1%7D%7B2%7D%20%26%20%5Cfrac%7B1%7D%7B2%7D%20%5C%5C%20%5Cfrac%7B1%7D%7B2%7D%20%26%20%5Cfrac%7B1%7D%7B2%7D%5Cend%7Bbmatrix%7D%5Cbegin%7Bbmatrix%7Dx%20%26%20x%20%5C%5C%20x%20%26%20x%5Cend%7Bbmatrix%7D%3DM

%5Ctherefore%5C%2C%20M%20P%3DM%3DP%20M

Chapter Questions
1 MCQs