If A E Mnxn (R), and A-¹ = A', then [det(A) | = 1 9. If A € Mnxn (R), and A-¹ = A', then A is diagonalizable. 10. If A E Mxn (R) and A-1 = A. If (v₁...₁) is an orthogonal basis for R", then (Av₁... A v) is an orthogonal basis for R". 11. If A € Mnxn (R), and Ax|| = |x|| vx E R", then A is diagonalizable. 12. If A € Mnxn (R), and (Ax, Ay) = (x,y) vx, y € R", then then A is diagonalizable. 13. If A is diagonalizable and invertible, then A¹ is diagonalizable. 14. If A E Mxn (R), then 3 an orthonormal matrix P and an upper triangular U, s.t. A = PUPt.