Failed installing Arch Linux....tried installing it three times
But at every boot what I get is Black screen with the cursor (underscore) blinking on it

I followed their official installation guide

Do anyone know how to resolve this problem?

I'll argue that the only thing that makes arch tricky to install is how you have the freedom to configure how it should boot.

The thing that got me in trouble the most was that I would go to guides talking about legacy bios or MBR to troubleshoot an install based on UEFI and GPT. You don't need to know what they are indepth, but you won't get away with mixing them up.

It's hard to troubleshoot based on your post, but my first instinct is to boot from the live usb again, mount your partitions, arch-chroot into /mnt, and check if your boot partition and boot loader is configured properly.

Try sticking to the official guide as much as you can, and pay close attention to which steps are for special cases that might not apply to you.

@Haxk20 @irene no I didn't get the grub screen...though I installed the grub and there were not any errors

Take the Windows 10 install software, start up, follow prompts, problem solved.

@Haxk20 grub-install --target=x86_64-efi --efi-directory=/boot --bootloader-id=GRUB

@iAmNaN 😂

@Ganofins I just couldn't help myself. It felt so... necessary... 👹

One does not simply install Arch Linux! Knowing this, I haven't attempted to yet. Lol so I can't help with this issue you're having.

@irene @Haxk20 @ltlian I again installed the arch now with mbr partitioning....now it is booting to grub rescue mode
Now I am stuck over there

You misunderstood. The black screen is arch linux, you have to personally develop all the features you want. Freedom they said

@crisz lol

@Haxk20 sorry I forgot to tell you my pc have BIOS firmware...so I used this --- grub-install --target=i386-pc /dev/sda. And then used grub-mkconfig -o /boot/grub/grub.cfg and after rebooting the pc what I get into is grub rescue mode

@Haxk20 I again installed the grub and generated the grub configuration and it worked, I successfully booted to Arch... finally
Thanks