No. you can not install selenium IDE for chrome or internet Explorer. Selenium IDE is only for FireFox.
You can run your testcase generated using selenium IDE in chrome or IE.
you need-
1- Selenium-standlone-server-2.XX.X.jar
2- IEDriverServer.exe
3- Selenium IDE for firefox
Lets put these files with extraction on d:\temp folder
open Command prompt and type
go to d:\ using cd d:\
d:\ go to folder temp using
d:\ cd temp
d:\temp> then type
d:\temp>java -jar Selenium-Standlone-Server-2.XX.X.jar -Dwebdriver.ie.driver=.\IEDriverServer.exe
server will get start
go to firefox->select selenium IDE->Open it->select option menu->select options-> select wedriver tab->check enableplay back web driver and put internet explorer browser name below instead of firefox
restart the Selenium IDE
create- record the test
execute the test will execute in Internet Explorer.