# 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\$?

Math 210-01: Linear Algebra: Reading Homework 2.2