Matriz diagonal:

A=DiagonalMatrix[{-2,0,Pi/3,-(5/2),7}]
MatrixForm[A]

Matriz nula:

B=ConstantArray[0,{5,5}]
B//MatrixForm

Matriz triangular superior:

A=UpperTriangularize[{{-7,-3,-7,-7/10,1},{0,-6,5/2,-1,2},{0,0,0,-9/8,-9},{0,0,0,-E,5/3},{0,0,0,0,4/9}}/.{0->1}]
MatrixForm[A]

Matriz triangular inferior:

A=UpperTriangularize[{{9,0,0,0,0},{5,-10,0,0,0},{1/4,-7,-8/3,0,0},{6,-2,9,1/2,0},{-2,-9,6,6,-6}}/.{0->1}]
MatrixForm[A]

Matriz simétrica:

A=(({{6, -4, -3, -3, -9}, {-4, 0, -1, 4, 3/5}, {-3, -1, 1/3, -2, 5}, {-3, 4, -2, 4, -3}, {-9, 3/5, 5, -3, 0}}));
A==Transpose[A]

Matriz antisimétrica:

A=(({{0, -3, -5, -10, -5}, {3, 0, 10, -4, -2}, {5, -10, 0, 6, -5}, {10, 4, -6, 0, -10}, {5, 2, 5, 10, 0}}));
Transpose[A]==-A

Matriz identidad y escalar:

IdentityMatrix[5]
MatrixForm[%]
MatrixForm[5IdentityMatrix[5]]