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1. Definition

2. Order of a matrix

3. Types of matrices

3.1. Column matrix

3.2. Row matrix

3.3. Square matrix

3.4. Diagonal matrix

3.5. Scalar matrix

3.6. Identity matrix

3.7. Zero matrix

3.8. Equality of matrices

3.9. Operation of matrices

3.9.1. Addition of matrices

3.9.2. Multiplication of a matrix by a scalar Negative of a matrix Difference of matrices Properties of matrix addition Commutative law Associative law Existence of additive identity The existence of additive inverse Properties of scalar multiplication of a matrix Multiplication of matrices Non-commutativity of multiplication of matrices Zero matrix as the product of two non-zero matrices Properties of multiplication of matrices The associative law The distributive law The existence of multiplicative identity

3.9.3. Transpose of a matrix Properties of transpose of the matrices

3.10. Symmetric and skew symmetric matrices

3.11. Invertible matrices

3.11.1. Inverse of a matrix by elementary operations

4. Elementary operation (transformation) of a matrix