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.
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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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