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both A and B are non - singular A is non - singular and B is singular A is singular and B is non - singular either A = 0 or B = 0 or both A and B are singular matrices

**Definitions; matrix representation; rows; column or general element**

**Row matrix and column matrix**

**Square matrix and diagonal matrix**

**Scalar matrix and identity matrix**

**Null matrix upper triangular matrix and lower triangular matrix**

**Symmetric matrix**

**skew symmetric matrix**

**Let `A` and `B` be symmetric matrices of same order. Then `A+B` is a symmetric matrix, `AB-BA` is a skew symmetric matrix and `AB+BA` is a symmetric matrix**

**Every matrix can be represented as a sum of symmetric and skew symmetric matrices**

**Singular matrix and Non-Singular Matrix**