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How to find an example of a 6 by 6 matrix which is similar to its inverse?

How to find an example of a 6 by 6 matrix which is similar to its inverse? I am trying to find one such example in Sage. Please give some idea to proceed.

How to find an example of a 6 by 6 matrix which is similar to its inverse?

How to find an example of a 6 by 6 matrix which is similar to its inverse? I am trying to find one such example in Sage. Please give some idea to proceed.

How to find an example of a 6 by 6 symmetric matrix which is similar to its inverse?

How to find an example of a 6 by 6 symmetric matrix which is similar to its inverse? I am trying to find one such example in Sage. Please give some idea to proceed.

How to find an example of a 6 by 6 symmetric matrix which is similar to its inverse?

How to find an example of a 6 by 6 symmetric matrix which is similar to its inverse? I am trying to find one such example in Sage. Please give some idea to proceed.

How to find an example of a 6 by 6 symmetric matrix (which is not identity matrix and does not satisfy A2= Identity matrix) which is similar to its inverse?

How to find an example of a 6 by 6 symmetric matrix which (which is not identity matrix and does not satisfy A2= Identity matrix)which is similar to its inverse? I am trying to find one such example in Sage. Please give some idea to proceed.