1. Order of a matrix
2. Elementary operation (transformation) of a matrix
3. Definition
4. Types of matrices
4.1. Column matrix
4.2. Row matrix
4.3. Square matrix
4.4. Diagonal matrix
4.5. Scalar matrix
4.6. Identity matrix
4.7. Zero matrix
4.8. Equality of matrices
4.9. Operation of matrices
4.9.1. Addition of matrices
4.9.2. Multiplication of a matrix by a scalar
4.9.2.1. Negative of a matrix
4.9.2.2. Difference of matrices
4.9.2.3. Properties of matrix addition
4.9.2.3.1. Commutative law
4.9.2.3.2. Associative law
4.9.2.3.3. Existence of additive identity
4.9.2.3.4. The existence of additive inverse
4.9.2.4. Properties of scalar multiplication of a matrix
4.9.2.5. Multiplication of matrices
4.9.2.5.1. Non-commutativity of multiplication of matrices
4.9.2.5.2. Zero matrix as the product of two non-zero matrices
4.9.2.6. Properties of multiplication of matrices
4.9.2.6.1. The associative law
4.9.2.6.2. The distributive law
4.9.2.6.3. The existence of multiplicative identity
4.9.3. Transpose of a matrix
4.9.3.1. Properties of transpose of the matrices
4.10. Symmetric and skew symmetric matrices
4.11. Invertible matrices
4.11.1. Inverse of a matrix by elementary operations