If (G,X) be the group of all real 2 x 2 matrices (b) such that ad - bc #0 with matrix multiplication operation. And (G',) be the group of all non-zero real numbers under multiplication. Define f = G→ G' by

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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If (G,×) be the group of all real 2 x 2 matrices
s (" ) such that ad – bc # 0 with
matrix multiplication operation. And (G',;) be the group of all non-zero real numbers
under multiplication. Define f = G → G' by
= ab – cd. Then
shoose
1- f is endomorphism.
2- f is homomorphism.
3- f is not homomorphism.
4- f is automorphism.
Transcribed Image Text:If (G,×) be the group of all real 2 x 2 matrices s (" ) such that ad – bc # 0 with matrix multiplication operation. And (G',;) be the group of all non-zero real numbers under multiplication. Define f = G → G' by = ab – cd. Then shoose 1- f is endomorphism. 2- f is homomorphism. 3- f is not homomorphism. 4- f is automorphism.
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