Matrices and matrix operations

with(LinearAlgebra);

Here are several ways to define matrices:

A1:=Matrix([[2,1,0,3],[-1,0,2,4],[4,-2,7,0]]);

A2:=Array([[2,1,0,3],[-1,0,2,4],[4,-2,7,0]]);

A3:=<<2,-1,4>|<1,0,-2>|<0,2,7>|<3,4,0>>;

A4:=Matrix(3,4,[[2,1,0,3],[-1,0,2,4],[4,-2,7,0]]);

I3:=IdentityMatrix(3);

I4:=IdentityMatrix(5);

Multiply(I3,A4);

Multiply(A4,I3);

Finding the transpose of a matrix.

A3t:=Transpose(A3);

Let us multiply the matrix A3 with its transpose A3t, and also A3t with A3.

B1:=Multiply(A3,A3t);

B2=Multiply(A3t,A3);

As you can see the two products are not the same.