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Types of Matrices:


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



Row matrix: A matrix is said to be a row matrix if it has only one row.



Square matrix: A matrix in which the number of rows are equal to the number of columns, is said to be a square matrix. Thus an m × n matrix is said to be a square matrix if m = n and is known as a square matrix of order ‘n’.





(iv) Diagonal matrix: A square matrix B = [bij]m × m is said to be a diagonal matrix if all its non diagonal elements are zero, that is a matrix B = [bij]m × m is said to be a diagonal matrix if bij = 0, when i ≠ j.




(v) Scalar matrix: A diagonal matrix is said to be a scalar matrix if its diagonal elements are equal, that is, a square matrix B = [bij]n × n is said to be a scalar matrix if
bij = 0, when i ≠ j
bij = k, when i = j, for some constant k.



(vi) Identity matrix: A square matrix in which elements in the diagonal are all 1 and rest are all zero is called an identity matrix. In other words, the square matrix A = [aij]n × n is an 1 if 0 if identity matrix, if
𝒂_𝒊𝒋= {█(𝟏, 𝒊𝒇 𝒊=𝒋@&𝟎, 𝒊𝒇 𝒊 ≠𝒋)┤
We denote the identity matrix of order n by In . When order is clear from the context, we simply write it as I.



(vii) Zero matrix: A matrix is said to be zero matrix or null matrix if all its elements are zero.


Equality of matrices:

Definition 2:
Two matrices A = [aij] and B = [bij] are said to be equal if
they are of the same order
each element of A is equal to the corresponding element of B, that is aij = bij for all i and j.



Elements:
The individual entries within the matrix are called elements. They can be numbers, variables, or other mathematical expressions.


Order:
The size or order of a matrix is expressed as "rows x columns" (e.g., a 2x2 matrix, a 3x1 matrix).