Question

) Let M 2 (R) be the set of all matrices of the form [a,b,c,d] (2X2 form), where a, b, c and
d are real numbers. Show that (M2 (R),+) is a group, where + denotes matrix addition.

Answer 1

Answer:

The number of matrices  formed = 4 + 4 = 8

Step-by-step explanation:

From the above question:

Let M 2 (R) be the set of all matrices of the form [a,b,c,d] (2X2 form), where a, b, c and d are real numbers.

Matrix M =    [  -a/b       -b/a ]

Here we need to show that (M2 (R),+) is a group, where + denotes matrix addition.

Thus ,

Conjugate of  a  =  -1/b and

Conjugate of b = -1/a

Thus Clearly,

      Two Conjugates are  -1/b and -1/a

either ad =1,

          bc = 0  or

          ad = 0,

          bc = 1

          ad = 1,

          bc = 0

This can be chosen in 4 ways

similarly ad=0,bc=1 can be chosen in 4 ways

so number of matrices  formed = 4 + 4 = 8.

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