ARM sells cores not chips, what resides at that address depends on the chip vendor that has bought the ARM core and put it in their chip. Implementations vary from vendor to vendor, chip to chip.
Traditionally an ARM will boot from address zero, more correctly the reset exception vector is at address zero. Unlike other processor families, the traditional ARM model is NOT a list of addresses for exception entry points but instead the ARM EXECUTES the instruction at that address, which means you need to use either a relative branch or a load pc instruction. The newer cortex-m series, which are thumb/thumb2 only (they cannot execute ARM (32 bit) instructions) uses the traditional (non-ARM) like list of addresses, also the zero address is not an exception vector, it is the address to load in the stack pointer, then the second entry is reset and so on. Also the cortex-m exception list is different, that family has like 128 individual interrupts, where the traditional ARM has two, fast and normal. There is a recent cortex-m based question or perhaps phrased as thumb2 question for running linux on a thumb2 ARM. I think the cortex-m implementations are all microcontroller class chips and only have on chip memory in the tens of kbytes, basically these dont fall into the category you are asking about. And you are asking about cortex-a9 anyway.
A number of cores or maybe all of them have a boot option where the boot address can be 0x00000000 or something like 0xFFFF0000 as an alternate address. using that would be very confusing for ARM users, but it provides the ability for example to have a rom at one address and a ram at another allowing you to boot on power up from a rom then switch the exception table into ram for runtime operation. You probably have a chip with a core that can do this but it is up to the chip vendor whether or not to use these edge of the core features or to hardwire them to some setting and not provide you that flexibility.
You need to look at the datasheet/docs for the chip in question. Find out what the name of the ARM core is, as you mentioned cortex-a9. Ideally you want to know the rev as well r0p0 kind of a thing, then go to ARM's website and find the TRM, technical reference manual for that core. You will also want to get a copy of the ARM ARM, ARM Architectural Reference Manual. The (traditional) ARM exception vectors are described in the ARM ARM as well as quite a ton more info. You also need the chip vendors documentation, and look into their boot scheme. Some will point address zero to the boot prom on power up, then the bootloader will need to do something, flip a bit in a register, and the memory controller will switch address 0 to ram. Some might have address 0 always configured as ram, and some other address always configured as rom, lets say 0x80000000 for example, and the chip will copy some items from rom to ram for you before boot, or the chip may simply have the power up setting for the reset vector to be a branch to rom, then it is up to the bootloader to patch up the vector table. As many different schemes as you can think of, it is likely someone has tried it, so you have to study the chip vendors documentation or sample code to understand Basically the answer to your rom question, is it depends and you have to check with the chip vendor.
The ARM TRM for the core should describe, if any, the strap options on the core (like being able to boot from an alternate address), connect those strap options, if any, that are implemented by the vendor. The ARM ARM is not really going to get into that like the TRM. A vendor worth buying from though will have some of their own documentation and/or code that shows what their rom based boot strategy is.
For a system destined to be a linux system you are going to have a bootloader, some non-linux code (very much like the bios on your desktop/laptop) that brings up the system and eventually launches linux. Linux is going to need a fair amount of memory (relative to microcontroller and other well known ARM implementations), that ram may end up being sram or dram and the bootloader may have to initialize the memory interface before it can start linux up. There are popular bootloaders like redboot and uboot. both are significant overkill, but provide features for developers and users like being able to re-flash linux, etc.
ARM linux has ATAGs (ARM TAGs). You can use both the traditional linux command line to tell linux boot information like what address to find the root file system, and ATAGs. Atags are structures in memory that I think r0 or something like that is set to when you branch from the bootloader to linux. The general concept though is the chip powers up, boots from rom or ram, if prepares ram so that it is ready to use, linux might want/need to be copied from rom to ram, the root file system, if separate, might want to be copied to somewhere else in ram. ATAGs are prepared to tell arm where to decompress linux if need be, as well as where to find the command line and or where to find things like the root file system, some registers are prepared as passed parameters to linux and lastly the bootloader branches to the address containing the entry point in the linux kernel.
