Prove that there exists a real second-order square matrix A

[Guest]

Is there a man who can solve this proof problem?

X is a second-order square matrix of any real number.
Prove that there exists a real second-order square matrix A, B, and C such that X=(A^2)+(B^2)+(C^2).

[HallsofIvy]

Is there a man who can solve this proof problem?

You don't think a woman could answer?

X is a second-order square matrix of any real number.
Prove that there exists a real second-order square matrix A, B, and C such that X=(A^2)+(B^2)+(C^2).

This isn't very clear. I know what a "second-order square matrix" is but I'm not clear on what ''of any real number" means. Do you mean "of any real numbers"- that it is a real matrix.

Then you say "There exist a real second-order square matrix A, B, and C". Those are three matrices! Did you mean three matrices, A, B, and C?