If `X={:[(1,-3,-4),(-1,3,4),(1,-3,-4)],` show that, `X^(2)=0` where 0 is the null matrix of order `3xx3.`

If A={:[(2,-3,-5),(-1,4,5),(1,-3,-4)]:} and B={:[(-1,3,5),(1,-3,-5),(-1,3,5)]:} show that AB = BA = 0, where 0 is the zero matrix of order 3xx3 .

If A={:[(1,x,-2),(2,2,4),(0,0,2)]:} and A^(2)+2I_(3)=3A find x, here I_(3) is the unit matrix of order 3.

If A=[(3,-3,4),(2,-3,4),(0,-1,1)]2-3 41 then show that A^-1=A^1.

If A= [(3,4),(4,-3)] find x if det|A-xI| =0,where I is a unit matrix of order 2.

If A = [(2,0,1),(0,-3,0),(0,0,4)] , verify A^(3) - 3A^(2) - 10A + 24I = 0 where 0 is zero matrix of order 3 xx 3 .

For the matrix A = [(3,-3,4),(2,-3,4),(0,-1,1)] , show that A^3 = A^-1

If A = [[1,x,-2],[2,2,4],[0,0,2]] and A^2+2I_3=3A Find x, here I_3 is the unit matrix of order 3.

If A=[[1,x,-2],[2,2,4],[0,0,2]] and A^2+2I_3=3A find x: here I_3 is the unit matrix of order 3.

If A=[122212221], then show that A^(2)-4A-5I=O, where Iand 0 are the unit matrix and the null matrix of order 3, respectively.Use this result to find A^(-1)

If x!=0 and |(1,x,2x),(1,3x,5x),(1,3,4)|=0 then x=