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 = [(2,2),(4,3)] show that, A A^(-1) =I_(2) wher I_(2) is the unit matrix of order 2.

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 = [[2,2],[4,3]] show that A A^(-1) = I_2 where I_2 is the unit matrix of order 2.

If A={:[(1,2,5),(-1,3,-4)]:} and B={:[(3,-2,1),(0,-1,4),(5,2,-1)]:}, show that, (AB)^(T)=B^(T)A^(T) where A^(T) is the transpose of A.

If A={:[(-2,1,3),(0,4,-1)]and B={:[(2,1),(-3,0),(4,-5)], show that, (AB)' = B'A' where A' is the transpose of A.

If A=({:(2,-1),(-1,2):}) " and " A^(2)-4A+3I=0 where I is the unit matrix of order 2, then find A^(-1) .

If A=[(1,2,3),(3,-2,1),(4,2,1)] , then show that A^(3)-23A-40I=0

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 |(-1,7,0),(2,1,-3),(3,4,1)|=A . Then |(13,-11,5),(-7,-1,25),(-21,-3,-15)| is ( I_(3) denotes the det of the identity matrix of order 3)