If `A={:((3,2),(3,3))and B={:((1,-2/3),(-1,1))` show that `AB=I_(2)` where `I_(2)` is the unit matrix of order 2.

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

If A = ((2,1),(3,4)) and B = ((1,-2),(-1,1)) show that, (AB)^(-1) = B^(-1) A^(-1)

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 = [(4,1),(7,2)] find a matrix B such that AB = I where I is the unit matrix of order 2.

If A = [[4,5],[5,6]] , show that A^2 = 10A + I where I is the unit matrix of order 2.

If A={:((1,2),(-1,-2))and B={:((-1,3),(-3,1)). then show that, (A+B)^(2)ne A^(2)+2AB+B^(2).

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={:[(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.