Operations $($regardless of structure$)$ fall into certain categories, three of which are defined

below:

a$.$ Unary operators $$ require one object on which to operate

b$.$ Binary operators: require two objects on which to operate

c$.$ Commutative operators: binary operators that evaluate to the same result regardless of

the order of the objects which are being operated on

Fill in the table below to categorize the matrix operations:

Operator Unary $($Y$/$N$)$ Binary $($Y$/$N$)$ Commutative $($Y$/$N$)$

Transposition

Addition

Multiplication

Join

Meet

Boolean product

Scalar multiplication

$2.$ If M is a $3\backslash$times $5$ matrix:

a$.$ Find the matrix A that would satisfy the following:

AM $=$ M

b$.$ Find the matrix B that would satisfy the following:

MB $=$ M