Definitions [1]
Definition: Matrix
A matrix is a rectangular arrangement of numbers arranged in rows and columns, enclosed in brackets [ ] or parentheses ( ).
Elements (Entries) of a Matrix
- Each number in a matrix is called an element (or entry).
Rows and Columns
- Horizontal lines → rows
- Vertical lines → columns
Order of a Matrix
- Order = number of rows × number of columns
- Written as m × n and read as “m by n”
Key Points
Key Points: Properties of Matrix Multiplication
| Property | Rule / Statement |
|---|---|
| Compatibility Rule | Matrices A and B can be multiplied only if the columns of A = the rows of B |
| Order of Product | If A is m × n and B is n × p, then AB is m × p |
| Non-Commutative | AB `\cancel(=)` BA (in general) |
| Associative Property | A(BC) = (AB)C |
| Distributive over Addition | A(B + C) = AB + AC |
| Zero Matrix Property | The product of two non-zero matrices can be a zero matrix |
| Cancellation Law | If AB = AC, it does not imply B = C |
| Identity Matrix | AI = IA = A (orders compatible) |
