1. Matrix Operations Add and Subtract Matrices Multiply Matrices
Determinants and Inverses
Properties of Real numbers and Matrices

2. Add and Subtract *Only when the matrices have the same dimensions
*Add or subtract the numbers that are in the same place
*When you subtract matrices, add the opposite (change the signs in the 2nd matrix)

3. Multiplying Matrices 2 x 3 3 x 5
The underlined diagonal has to match, the other numbers tell you what dimensions the new matrix will be (2x5)
Draw the new matrix with blanks
Multiply row by column (add the #’s)

4. Determinants and Inverses
[a b] *cross multiply and subtract
[c d] (a*d) – (b*c) = |determinant|
Inverses ( −1 )
Find the determinant
Switch a and d
Change the sign of b and c
Divide all numbers by the determinent

5. Properties The ones that work for matrices
Associative Property of Addition
Commutative Property of Addition
Additive Identity
Distributive Property
The ones that DON’T work for matrices
Associative Property of Multiplication
Commutative Property of Multiplication
Sometimes works – Multiplicative Identity (only works with square matrices)