Matrices
IMPORTANT You will need to have a WolframAlpha Pro account to use Wolfram effectively.
Wolfram has it’s own documentation.
Writing a Matrix
In WolframAlpha, matrices are written with curly brackets for each horizontal row, with rows separated by commas, and a pair of curly brackets surrounding the entire matrix.
Addition & Multiplication
Addition, multiplication and scalar multiplication work pretty much as you would expect them to. Addition uses a + between matrices, and multiplication needs a . or a *
Operations
Finding the determinant, minors, cofactors or inverse of a matrix is as simple as typing determinant, minors, cofactors or inverse, followed by the matrix itself.
Simultaneous Equations
Wolfram can also solve simultaneous equations in matrix form (linear systems). You can do this, as above, by simply leaving the unknows in the matrix as letters.
You can also solve by rearranging the equation: these will give identical results. The rearrangement is computing the inverse of the matrix form with the equation coefficients, and then do a matrix-vector multiplication to obtain the solution vector. It’s usually easier to let Wolfram do the algebra for you, though.