1. The problem statement, all variables and given/known data Without expanding the determinant show that bc a^2 a^2 b^2 ca b^2 c^2 c^2 ab = bc ab ca ab ca bc ca bc ab 2. Relevant equations 3. Attempt at solution Well, one thing I noticed is that the diagonal row all contain the same values (bc, ca, ab) Using the first determinant, we can simplify it to bc |ca b^2| - ca|bc a^2| + ab |bc a^2| ....|c^2 ab|......|c^2 ab|.........|b^2 ca| the second determinant would be bc |ca bc| - ca |bc ca| + ab|bc ab| ....|bc ab|........|ca ab|........|ab ca| obviously its easy to see that these two determinants are identical, but is this what the question asks? It says to show without expanding, so I'm not sure if there's another way to show this.