# Revision history [back]

Use block_matrix to insure the result is an element of $M_{4\times 4}$ (over the ring SR) and not of $M_{2\times 2}$ with entries in a matrix ring, which is a non-commutative ring, and where strictly speaking the inverse is not implemented.

For instance:

sage: D = block_matrix( 2, 2, [A, B, B.T, C] )
sage: D
[a1 b1|a2 b2]
[c1 d1|c2 d2]
[-----+-----]
[a2 c2|a3 b3]
[b2 d2|c3 d3]
sage: D.is_invertible()
True
sage: DI = D.inverse()


So DI could be computed and we have:

sage: (DI*D).simplify_full()
[1 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1]