noun (plural matrices | ˈmeɪtrɪsiːz | or matrixes) 

1 the cultural, social, or political environment in which something develops: Oxbridge was the matrix of the ideology. 

₂ a mass of fine-grained rock in which gems, crystals, or fossils are embedded: nodules of secondary limestone set in a matrix of porous dolomite | [mass noun] : such fossils will often be partly concealed by matrix. • Biology the substance between cells or in which structures are embedded: the lipid matrix of olfactory cells. • fine material used to bind together the coarser particles of a composite substance: the matrix of gravel paths is hoed regularly. 

3 a mould in which something, such as a record or printing type, is cast or shaped: her two duets with Isobel Baillie were never issued and the matrices were destroyed. 

4 Mathematics a rectangular array of quantities or expressions in rows and columns that is treated as a single entity and manipulated according to particular rules: this formula applies for all square matrices. • a grid-like arrangement of elements; a lattice: a sparse matrix is a data structure in which few of the potential elements are filled out. 

5 an organizational structure in which two or more lines of command, responsibility, or communication may run through the same individual: [as modifier] :  matrix structures are said to foster greater flexibility.
Oxford Dictionary
https://www.slideshare.net/AdilAslam4/matrices-in-discrete-mathematics-and-its-applications

Columns Matrix

Rectangular Matrix

Square Matrix

Diagonal Matrix

Scalar Matrix

Identity Matrix

Triangular Matrix

Null or Zero Matrix

Transpose of a Matrix

e.g.

A=[123]A=[123]

Column Matrix:
A matrix is said to be a column matrix if it has only one column.

e.g.

B=⎡⎣⎢⎢123⎤⎦⎥⎥B=[123]

Rectangular Matrix:
A matrix is said to be rectangular if the number of rows is not equal to the number of columns.

e.g.

A=[123542]A=[134252]

Square Matrix:
A matrix is said to be square if the number of rows is equal to the number of columns.

e.g.

B=⎡⎣⎢⎢151329446⎤⎦⎥⎥B=[134524196]

Diagonal Matrix:
A square matrix is said to be diagonal if at least one element of principal diagonal is non-zero and all the other elements are zero.

e.g.

D=⎡⎣⎢⎢100020003⎤⎦⎥⎥D=[100020003]

Scalar Matrix:
A diagonal matrix is said to be scalar if all of its diagonal elements are the same.

e.g.

A=⎡⎣⎢⎢200020002⎤⎦⎥⎥A=[200020002]

Identity or Unit Matrix:
A diagonal matrix is said to be identity if all of its diagonal elements are equal to one, denoted by II.

e.g.

I=[1001],I=⎡⎣⎢⎢100010001⎤⎦⎥⎥I=[1001],I=[100010001]

Triangular Matrix:
A square matrix is said to be triangular if all of its elements above the principal diagonal are zero (lower triangular matrix) or all of its elements below the principal diagonal are zero (upper triangular matrix).

e.g:

A=⎡⎣⎢⎢123045006⎤⎦⎥⎥A=[100240356]

! (Lower Triangular Matrix)

B=⎡⎣⎢⎢500810327⎤⎦⎥⎥B=[583012007]

(Upper Triangular Matrix)

Null or Zero Matrix:
A matrix is said to be a null or zero matrix if all of its elements are equal to zero. It is denoted by OO.

e.g.

O=[0000],O=⎡⎣⎢⎢000000000⎤⎦⎥⎥O=[0000],O=[000000000]

Transpose of a Matrix:
Suppose AA is a given matrix, then the matrix obtained by interchanging its rows into columns is called the transpose of AA. It is denoted by AtAt.

e.g.
Let

A=[182436]A=[123846]

then

At=⎡⎣⎢⎢123846⎤⎦⎥⎥

Read more: https://www.emathzone.com/tutorials/algebra/types-of-matrices.html#ixzz5i6HlBReG

[ 1  9  13 ]
[ 20 5 -6 ]

 
A Matrix
(This one has 2 Rows and 3 Columns)

Read more: https://www.emathzone.com/tutorials/algebra/types-of-matrices.html#ixzz5i6JUOMbv

{\displaystyle {\begin{bmatrix}1&9&-13\\20&5&-6\end{bmatrix}}.}