Math 210-01: Linear Algebra: Reading Homework 2.2

1. Properties of Matrix Operations : what is being developed in this section?
   
   1. Properties of Addition : what are the properties introduced? how does the associative property extend a binary operation?
      
      1. additive identity : what matrix is the identity under matrix addition?
         
      2. additive inverse : what matrix is the inverse under matrix addition?
         
      3. matrix equations : to what extent do standard algebraic solution techniques apply to matrix equations?
         
   2. Properties of Multiplication : how are the properties introduced for matrix multiplication different than those for matrix addition?
      
      1. commutivity : is matrix multiplication commutative?
         
      2. cancellation : does $AB = CB$ imply that $A=C$ (where $A$, $B$, and $C$ are matrices?
         
      3. multiplicative identity : what matrix is the identity under matrix multiplication?
         
   3. Transposes : what is the transpose of a matrix? explain
      
      1. symmetry : what do we mean when we say a matrix is symmetric?
         
      2. properties of the transpose : what properties does the transpose have? in particular, what happens to $(AB)^T$?