Consider two matrices `B=[[1,0],[0,-1]]` and `C=[[0,1],[-1,0]].` If matrix `A=sum_(n=1)^(100)(B^(n)+C^(n))` ,then find the absolute value of determinant of matrix A.

Consider the matrix B= [[0,-1],[1,0]] ,then B^(1027)

Consider a matrix A=[[1,1,1],[0,0,1],[2,3,4]] . The value of determinant of (A^(-1)-(A^(-1))^(2)) is

Consider a matrix A=[[1,1,1],[0,0,1],[2,3,4]] .The value of determinant of (A^(-1)-(A^(-1))^(2)) is

Consider a matrix A= [[1,1,1],[0,0,1],[2,3,4]] .The value of determinant of (A^(-1)-(A^(-1))^(2)) is

If a_(n) = sum_(r=0)^(n) (1)/(""^(n)C_(r)) , find the value of sum_(r=0)^(n) (r)/(""^(n)C_(r))

i) Find the rank of the matrix [[1,0,0],[1,0,0],[0,0,1]]

If a+b=1, then sum_(n=0)^(n)C(n,r)a^(r)b^(n-r) is equal to '

If the product of n matrices [[1,10,1]][[1,20,1]][[1,30,1]]......[[1,n0,1]] is equal to the matrix ,[[1,3780,1]] then the value of n is equal to

Let A= [[1,0,0],[2,1,0],[3,2,1]] be a square matrix and C_(1), C_(2), C_(3) be three comumn matrices satisgying AC_(1) = [[1],[0],[0]], AC_(2) = [[2],[3],[0]] and AC_(3)= [[2],[3],[1]] of matrix B. If the matrix C= 1/3 (AcdotB). The ratio of the trace of the matrix B to the matrix C, is

If matrix [{:(0,a,3),(2,b,-1),(c,1,0):}] is skew-symmetric matrix, then find the values of a,b and c,