If `A=[(1,0,1),(0,1,2),(0,0,4)]`, show that `|3A|=27|A|`

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

If A[(-1,0),(0,1)] and B=[(0,1),(1,0)] , show that (A+B)^2 ne A^2+2AB+B^2 .

If A = [(2,3),(3,10)],I=[(1,0),(0,1)] then show that (2I -A) (10I-A) = 9I .

If A=[(1,2,3),(0,-4,2),(0,0,7)] , for what values of x, the matrix A-xI_3 is singular?

If A = [(0, 0, 1),(0, 1, 0),(1, 0, 0)] find A^2 .

If A = [(3, 1),(-1, 2)] show that A^2 - 5A + 7I = 0 .

If A=[(1,0,-1),(2,1,0)], B=[(3,1),(-1,2),(0,1)] and C=[(4,2),(-3,0),(1,2)] show that AB=AC .

If A=[(1,-3,2),(2,1,-3),(4,-3,-1)], B=[(1,4,1,0),(2,1,1,1),(1,-2,1,2)]and C=[(2,1,-1,-2),(3,-2,-1,-1),(2,-5,-1,0)] , show that AB=AC .

If F(x)=[(cosx,-sinx,0),(sinx,cosx,0),(0,0,1)] , show that F(x)*F(y)=F(x+y)

If A = [(2,3),(1, 2)] prove that A^3 - 4A^2 + A = 0