Question 376385
{{{det((matrix(3,3,0,1,1,1,0,1,1,1,0)) )= 2}}}.
We have to get {{{det((matrix(3,3, 0,ab^2,ac^2, a^2b,0, bc^2, a^2c, b^2c, 0)))}}}
Now factor {{{a^2}}} from the 1st column, {{{b^2}}} from the 2nd column, and {{{c^2}}} from the 3rd column, to get
{{{a^2b^2c^2det((matrix(3,3,0,a,a,b,0,b,c,c,0)))}}}.
Then factor a from the 1st row, b from the 2nd row, and c from the 3rd row, to get
{{{a^3b^3c^3det((matrix(3,3,0,1,1,1,0,1,1,1,0)))}}}.
Therefore the value of the determinant is {{{2a^3b^3c^3}}}.