Write a and b of order 3×3 such that AB=BA
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A and B are two matrices of order 3×3so that AB=A and BA=B then ... If A and B are two matrices such that AB=B and BA=A.
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αͷswϵr➜
ᴀ ᴀɴᴅ ʙ ᴀʀᴇ ᴛᴡᴏ sǫᴜᴀʀᴇ ᴍᴀᴛʀɪᴄᴇs ᴏғ ᴏʀᴅᴇʀ 3×3 ᴡʜɪᴄʜ sᴀᴛɪsғʏ ᴀʙ=ᴀ ᴀɴᴅ ʙᴀ=ʙ, ᴛʜᴇɴ ɪғ ᴍᴀᴛʀɪx ᴀ ɪs sɪɴɢᴜʟᴀʀ, ᴛʜᴇɴ ᴍᴀᴛʀɪx ʙ ɪs ᴀʟsᴏ sɪɴɢᴜʟᴀʀ .
ᴀ sɪɴɢᴜʟᴀʀ ᴍᴀᴛʀɪx ɪs ᴛʜᴀᴛ ᴍᴀᴛʀɪx ᴡʜᴏsᴇ ᴅᴇᴛᴇʀᴍɪɴᴀɴᴛs ɪs ᴢᴇʀᴏ ᴀɴᴅ ᴡʜɪᴄʜ ɪs ɴᴏɴ-ɪʀʀᴇᴠᴇʀsɪʙʟᴇ.
∴ᴀ ᴀɴᴅ ʙ ʙᴏᴛʜ ᴀʀᴇ sɪɴɢᴜʟᴀʀ ᴍᴀᴛʀɪᴄᴇs, ᴛʜᴇɴ ᴏɴʟʏ ᴛʜᴇ ᴄᴏɴᴅɪᴛɪᴏɴs ᴀʙ=ᴀ ᴀɴᴅ ʙᴀ=ʙ ʜᴏʟᴅs ᴛʀᴜᴇ.
ʜᴇɴᴄᴇ, ᴛʜᴇ ᴀɴsᴡᴇʀ ɪs ɪғ ᴍᴀᴛʀɪx ᴀ ɪs sɪɴɢᴜʟᴀʀ, ᴛʜᴇɴ ᴍᴀᴛʀɪx ʙ ɪs ᴀʟsᴏ sɪɴɢᴜʟᴀʀ.
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