If A=`((1,0,0),(2,3,4),(5,-6,x))` and "det=45" then the value of "x" is

If {:[(4,5)]:}{:[(1,6),(x,3)]:}{:[(-2),(3)]:}=[9] , then the value of x is

If |{:(x, 2, 3),(2,3,x),(3 , x,2):}| = |{:(1, x, 4),(x,4,1),(4 , 1,x):}| = |{:(0, 5, x),(5,x,0),(x, 0,5):}| = 0, then the value x equals (x in R )

If the trace of the matrix A=({:(x-5,0,2,4),(3,x^(2)-10,6,1),(-2,3,x-7,1),(1,2,0,-2):}) assumes the value zero, then the value of x equals to

Given A=[[1,0,0],[0,-1,0],[0,0,-1]] and B=[[2,x,x],[x,4,5],[x,6,7]] : determine the value of x , if there be any , for which the property AB=BA may hold.

If one root of 2x^(2)-16x+k=0 lies in (3,4) and other root in (4,5), then the integral value of k is :

If A = [{:(2,3),(0,-1):}] , then the value of det (A^(4)) | det ( A^(10) - Adj( 2A))^(10)) is equal to "_______________" .