The square-bracket symbols   [   and   ]   denote matrices.
Elements in a row are separated by a comma.
Rows in a matrix are separated by a semi-colon.
For example, enter the following 2x2 matrix

m = [1, 2;  3, t]

Subsequently, other matrices may be defined in terms of   m,   e.g.,

twoByFourMatrix = [m, m]

To multiply the matrix   m   by the scalar 10 and divide by 2, type

mFive = 10 * m / 2                  

To add and multiply matrices   m   and   m,   type

add = m + m
multiply = m * m

To form the transpose and inverse of   m,   type

transpose = GetTranspose( m )
inverse = GetInverse( m )

To calculate the determinant and eigenvalues of   m,   type

determinant = GetDeterminant( m )
eigenvalues = GetEigen( m )

To find the ordinary time-derivative of the matrix  m,  type

matrixDerivative = Dt( m )

To get the element in the 1st-row and 2nd column of   m,   type
Alternatively, use the command  GetElement(1,2).

element12 = m[1,2]

To extract row 2 and columns 2 and 1 of   m,   type

row2 = GetRows( m, 2 )
column21 = GetColumns( m, 2, 1 )

To form the 3x3 identity matrix,   type

identity33 = GetIdentityMatrix(3,3)

To save input (for subsequent re-use) and/or input and output responses, type
Save   MatrixSampleCommands.txt
Save   MatrixSampleCommands.all

A description of many matrix commands is also available in pdf format.