The binary operation ltmath gt ltmrow gt ltmo gt* lt/mo gt ltmo gt: lt/mo gt ltmi gtR lt/mi

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Let ltmath gt ltmrow gt ltmi gtA lt/mi gt ltmo gt= lt/mo gt ltmi gtN lt/mi gt ltmo gtȢ

Let ltmath gt ltmrow gt ltmi gtA lt/mi gt ltmo gt= lt/mo gt ltmrow gt ltmo gt{ lt/mo gt

Define a binary operation * on the set ltmath gt ltmrow gt ltmi gtA lt/mi gt ltmo gt= lt

Let * be a binary operation defined by ltmath gt ltmrow gt ltmi gta lt/mi gt ltmo gt* lt

A binary operation * on ltmath gt ltmi gtZ lt/mi gt lt/math gt defined by ltmath gt lt

Let ltmath gt ltmrow gt ltmsub gt ltmi gtR lt/mi gt ltmn gt0 lt/mn gt lt/msub gt lt/mro

Let ltmath gt ltmrow gt ltmsub gt ltmi gtR lt/mi gt ltmn gt0 lt/mn gt lt/msub gt lt/mro

Find the total number of binary operations on ltmath gt ltmrow gt ltmrow gt ltmo gt{ lt/