If `([2,4],[-1,k])` is nil potent matrix of index `2` than k=

A=[[1,1,3],[5,2,6],[-2,-1,-3]] is a nilpotent matrix of index K .Then K=

Show that the matrix [{:( 1,1,3),( 5,2,6),( -2,-1,-3):}] is nilpotent matrix of index 3.

If A=[[2-k,2],[1,3-k]] is a singular matrix,then find the value of 5k-k^(2) .

Let A=[(2,0,7),(0,1,0),(1,-2,1)] and B=[(-k,14k,7k),(0,1,0),(k,-4k,-2k)] . If AB=I , where I is an identity matrix of order 3, then the sum of all elements of matrix B is equal to

If (2,k,-1) is the centroid of the triangle with vertices (2,-1,2), (1,-3,4) and (3,k,-1) , then k= _____.

If A^(k)= 0 (Ais nilpotent with index k), (I-A)^(p)=I+A+A^(2)+. . .+A^(k-1) , thus p is

If B=[{:(6,3),(-2,k):}] is singular matrix then the value of k is____

If A is a square matrix of order 2, |A| ne 0 and |4A| = k |A|, then the value of k is :

If A is a square matrix of order n xx n and k is a scalar, then adj (kA) is equal to (1) k adj A (2) k^n adj A (3) k^(n-1) adj A (4) k^(n+1) adj A