A matrix having m rows and n columns is called a  arraycolumn matrixdiagonal matrixidentity matrixinversematrix of ordernegativerow matrixscalar matrixskew symmetricsquare matrixsumsymmetrictransposeuniquezero matrix m × n.

A matrix is said to be a  arraycolumn matrixdiagonal matrixidentity matrixinversematrix of ordernegativerow matrixscalar matrixskew symmetricsquare matrixsumsymmetrictransposeuniquezero matrix if it has only one column.

A matrix is said to be a  arraycolumn matrixdiagonal matrixidentity matrixinversematrix of ordernegativerow matrixscalar matrixskew symmetricsquare matrixsumsymmetrictransposeuniquezero matrix if it has only one row.

A matrix in which the number of rows are equal to the number of columns, is said to be a  arraycolumn matrixdiagonal matrixidentity matrixinversematrix of ordernegativerow matrixscalar matrixskew symmetricsquare matrixsumsymmetrictransposeuniquezero matrix.

A square matrix is said to be a  arraycolumn matrixdiagonal matrixidentity matrixinversematrix of ordernegativerow matrixscalar matrixskew symmetricsquare matrixsumsymmetrictransposeuniquezero matrix if all its non diagonal elements are zero.

A diagonal matrix is said to be a  arraycolumn matrixdiagonal matrixidentity matrixinversematrix of ordernegativerow matrixscalar matrixskew symmetricsquare matrixsumsymmetrictransposeuniquezero matrix if its diagonal elements are equal.

A square matrix in which elements in the diagonal are all 1 and rest are all zero is called an  arraycolumn matrixdiagonal matrixidentity matrixinversematrix of ordernegativerow matrixscalar matrixskew symmetricsquare matrixsumsymmetrictransposeuniquezero matrix.

A matrix is said to be  arraycolumn matrixdiagonal matrixidentity matrixinversematrix of ordernegativerow matrixscalar matrixskew symmetricsquare matrixsumsymmetrictransposeuniquezero matrix if all its elements are zero.

The  arraycolumn matrixdiagonal matrixidentity matrixinversematrix of ordernegativerow matrixscalar matrixskew symmetricsquare matrixsumsymmetrictransposeuniquezero matrix of a matrix is denoted by – A.

If A = [aij] be an m × n matrix, then the matrix obtained by interchanging the rows and columns of A is called the  arraycolumn matrixdiagonal matrixidentity matrixinversematrix of ordernegativerow matrixscalar matrixskew symmetricsquare matrixsumsymmetrictransposeuniquezero matrix of A.

A square matrix A = [aij] is said to be  arraycolumn matrixdiagonal matrixidentity matrixinversematrix of ordernegativerow matrixscalar matrixskew symmetricsquare matrixsumsymmetrictransposeuniquezero matrix matrix if A′ = – A, that is aji = – aij for all possible values of i and j.

A square matrix A = [aij] is said to be  arraycolumn matrixdiagonal matrixidentity matrixinversematrix of ordernegativerow matrixscalar matrixskew symmetricsquare matrixsumsymmetrictransposeuniquezero matrix if A′ = A, that is, [aij] = [aji] for all possible values of i and j.

For any square matrix A with real number entries, A + A′ is a  arraycolumn matrixdiagonal matrixidentity matrixinversematrix of ordernegativerow matrixscalar matrixskew symmetricsquare matrixsumsymmetrictransposeuniquezero matrix matrix and A – A′ is a  arraycolumn matrixdiagonal matrixidentity matrixinversematrix of ordernegativerow matrixscalar matrixskew symmetricsquare matrixsumsymmetrictransposeuniquezero matrix matrix.

Any square matrix can be expressed as the  arraycolumn matrixdiagonal matrixidentity matrixinversematrix of ordernegativerow matrixscalar matrixskew symmetricsquare matrixsumsymmetrictransposeuniquezero matrix of a symmetric and a skew symmetric matrix.

If A is a square matrix of order m, and if there exists another square matrix B of the same order m, such that AB = BA = I, then B is called the  arraycolumn matrixdiagonal matrixidentity matrixinversematrix of ordernegativerow matrixscalar matrixskew symmetricsquare matrixsumsymmetrictransposeuniquezero matrix matrix of A.

A matrix is an ordered rectangular  arraycolumn matrixdiagonal matrixidentity matrixinversematrix of ordernegativerow matrixscalar matrixskew symmetricsquare matrixsumsymmetrictransposeuniquezero matrix of numbers or functions.

Inverse of a square matrix, if it exists, is  arraycolumn matrixdiagonal matrixidentity matrixinversematrix of ordernegativerow matrixscalar matrixskew symmetricsquare matrixsumsymmetrictransposeuniquezero matrix.