Matrices Cheat Sheet

Key Definitions

• Matrix: A rectangular array of numbers arranged in rows and columns. ✅

• Element: An individual number in a matrix. ✅

• Order of a Matrix: Given as m x n, where m = number of rows and n = number of columns. ✅

Important Concepts

Types of Matrices

• Row Matrix: A matrix with only one row. ✅

• Column Matrix: A matrix with only one column. ✅

• Square Matrix: A matrix with the same number of rows and columns. ✅

• Zero Matrix: A matrix where all elements are zero. ✅

• Identity Matrix: A square matrix with 1s on the diagonal and 0s elsewhere. ✅

Operations

• Addition: Add corresponding elements. Matrices must be of the same order. ✅

• Subtraction: Subtract corresponding elements. Matrices must be of the same order. ✅

• Multiplication: For matrices A (m x n) and B (n x p), the result is C (m x p). ✅

Key Formulas

• Matrix Addition:

• Matrix Multiplication:

Common Mistakes to Avoid

Common Mistake: Forgetting that matrix multiplication is not commutative (i.e., AB ≠ BA).

Memory Tricks

Tip: "RACE" —

• R: Row Matrix

• A: Addition

• C: Column Matrix

• E: Element

Key Diagrams

Matrix A (2x3):
| 1  2  3 |
| 4  5  6 |
Matrix B (2x3):
| 7  8  9 |
| 10 11 12 |
Matrix C (2x3) = A + B:
| 8 10 12 |
| 14 16 18 |