If (G,X) be the group of all real 2 x 2 matrices (“ ") such that ad - be + 0 with matrix multiplication operation. And (G',;) be the group of all non-zero real numbers under multiplication. Define f = G →G'by r(: ) = ab- cd. Then 1- f is endomorphism. 2- f is homomorphism. 3- f is not homomorphism. 4- / is automorphism.

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Chapter2: Second-order Linear Odes
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If (G,X) be the group of all real 2 × 2 matrices (" ) 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
s( ) = ab – cd. Then
1- f is endomorphism.
2- f is homomorphism.
3- f is not homomorphism.
4- f is automorphism.
1
2
4 O
Transcribed Image Text:If (G,X) be the group of all real 2 × 2 matrices (" ) 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 s( ) = ab – cd. Then 1- f is endomorphism. 2- f is homomorphism. 3- f is not homomorphism. 4- f is automorphism. 1 2 4 O
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