Let us create some 2x2 matrices:
a = {{a11, a12}, {a21, a22}};
b = {{b11, b12}, {b21, b22}};
c = {{c11, c12}, {c21, c22}};
d = {{d11, d12}, {d21, d22}};
You can visualize the combined object of depth four using
MatrixForm[{{a, b}, {c, d}}]
A possible way to construct the matrix by blocks is
m = ArrayFlatten[{{a, b}, {c, d}}]
Visualize it again with
MatrixForm[m]
Or compute eigenvalues with
Eigenvalues[m]
