# Matrix

A matrix is a rectangular array of numbers arranged into rows and columns.

**Types of Matrices**

**1. Row matrix**

A matrix having one row and any number of columns is a row matrix

E.g.: A = [a b c d]_{1xn}

**2. Column matrix**

A matrix having one column and any number of rows is known as column matrix.

**3.Zero matrix**

A zero or null matrix is one whose elements are zeroes.

**4. Square matrix**

A matrix having same number of rows and columns is known as a square matrix.

**5. Diagonal matrix**

A square matrix having non-zero entries only on the main diagonal is known as diagonal matrix.

**6. Scalar matrix**

A diagonal matrix with equal non-zero entries on the same diagonal is known as scalar matrix.

**7. Unit matrix (Identity matrix)**

A diagonal matrix is a unit matrix each of the diagonal elements is unity.

**Transpose of a matrix**

The transpose of a matrix A is the matrix obtained by interchanging the rows and columns of A, and is denoted by A^{1} or A^{T}.

(A^{1})^{1} = A

(A+B)^{1} = A^{1} + B^{1}

^{ }(AB)^{1} = B^{1}A^{1}

(kA)^{1} = kA^{1}, where k is a complex number

**Symmetric matrices**

A square matrix is said to be symmetric if A^{1} = A.

**Skew-Symmetric matrices**

A square matrix A is said to be skew-symmetric if A^{1} = -A.

**Determinants**

To each square matrix A = [aij] we associate a number called determinant of A and is denoted by |A|. Matrices which are not square do not have determinants.

**Singular and non-Singular matrices**

A square matrix A is called singular if |A| = 0. If |A| ¹ 0 then A is called non-singular.