# How Can I slove this problem in sage?

Sorry for my bad English.

**Problem**:

Write a procedure that accepts as input an orthogonal matrix A |- O(2m), with m >= 1, such that
** A^2= -I(2m)** [subscript 2m]

and give as output an orthonormal basis of R^2m type:

*u1,Au1,u2,Au2, ... , um,Aum`*

Test the procedure on matrices of type ** A = tMJM** [t apex] where

**is a random matrix and**

*M |- O(2M)***is the block matrix 2x2 all equal to**

*J |- O(2m)**J = [column 1] ( 0 1) [column 2] (-1 0)*

This looks like homework. If you want some help, you should ask more precise questions related to your research in solving those exercises, especially where you are locked.