Linear Algebra Puzzle 1

#LinearAlgebra #Matrix #MatrixAlgebra

[routemath]

Marcel on twitter posted a hint for a second solution. Here is my solution using his hint. Thanks, Marcel!

If A^2 = I then det(A^2) = (det A)^2 = det I = 1. So det A = +1 or -1. If det A = 1, we get x^3 + y^3 + z^3 = 5. If det A = -1, we get x^3 + y^3 + z^3 = 7 our solution from the video.