If `A=[(-1,1),(0,-2)]`, then prove that `A^(2)+3A+2I=O`. Further, find matrices B and C of order 2 with integer elements if `A=B^(3)+C^(3)`.

If A=[-1 1 0-2] , then prove that A^2+3A+2I=Odot Hence, find Ba n dC matrices of order 2 with integer elements, if A=B^3+C^3dot

If A=[{:(1,-1,1),(0,2,-3),(2,1,0):}] and B=(adjA) and C=5A , then find the value of (|adjB|)/(|C |)

If A=[(a,b),(c,d)] , where a, b, c and d are real numbers, then prove that A^(2)-(a+d)A+(ad-bc) I=O . Hence or therwise, prove that if A^(3)=O then A^(2)=O

Let for A=[(1,0,0),(2,1,0),(3,2,1)] , there be three row matrices R_(1), R_(2) and R_(3) , satifying the relations, R_(1)A=[(1,0,0)], R_(2)A=[(2,3,0)] and R_(3)A=[(2,3,1)] . If B is square matrix of order 3 with rows R_(1), R_(2) and R_(3) in order, then The value of det. (2A^(100) B^(3)-A^(99) B^(4)) is

If A and B are square matrices of orders 3 such that |A|=-2 and |B|=3 find the value of |3AB| .

If matrix A=[(0,1,-1),(4,-3,4),(3,-3,4)]=B+C , where B is symmetric matrix and C is skew-symmetric matrix, then find matrices B and C.

If A= [(2,1),(4,-2)] ,B= [(4,-2),(1,4)] and C= [(-2,-3),(1,2)] find (i)-2A+B+C

If A=(1)/(7)[{:(6,-3,a),(b,-2,6),(2,c,3):}] is orthogonal, find a, b and c and hence A^(-1) .

If a and B are square matrices of same order such that AB+BA=O , then prove that A^(3)-B^(3)=(A+B) (A^(2)-AB-B^(2)) .