If `|[4,1] , [2,1]|^2=|[3,2] , [1,x]|-|[x,3] , [-2,1]|` then `x=`

Answer the following: What is the value of x if [[4,1],[2,1]]^2=[[3,2],[1,x]]-[[x,3],[-2,1]] ?

If |{:(4,1),(2,1):}|^(2)=|{:(3,2),(1,x):}|-|{:(x,3),(-2,1):}| , then the value of x is :

|[3,x],[x,1]|= |[3,2],[4,1]| then x is equal to

If |[1,x,x^2] , [x,x^2,1] , [x^2,1,x]|=3 then find the value of |[x^3-1, 0, x-x^4] , [0,x-x^4, x^3-1] , [x-x^4, x^3-1, 0]|

If |[1,x,x^2] , [x,x^2,1] , [x^2,1,x]|=3 then find the value of |[x^3-1, 0, x-x^4] , [0,x-x^4, x^3-1] , [x-x^4, x^3-1, 0]|

If |(3,2),(1,x)|-|(2x,3),(-2,1)|=|(4.1,1),(2,1)|^(2) , then x=______

If X+Y=[[2,-1],[1,3],[-3,2]] and X-2Y=[[-2,-1],[-3,-1],[4,-2]] find X and Y.

Without expanding, show that the value of each of the determinants is zero: |[(2^x+2^(-x))^2, (2^x-2^(-1))^2, 1] , [(3^x+3^(-1))^2, (3^x-3^(-x))^2, 1] , [(4^x+4^(-x))^2, (4^x-4^(-x))^2, 1]|