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

If A=[{:(1,0,1),(0,1,2),(0,0,4):}] then show that [3A]=27[A]

If A=[{:(-1,2,0),(-1,1,1),(0,1,0):}] then show that A^(-1)=A^2

If iz^(3)+z^(2)-z+i=0 then show that |z|=1.

If A=[{:(2,3,-4),(5,1,0),(3,-2,5):}]andI=[{:(1,0,0),(0,1,0),(0,0,1):}] then show that AI=IA=A.

If A=[{:(1,2,1),(2,1,3),(1,1,0):}] then prove that A^3-2A^2-7A-4I_3=0 . Hence find A^(-1)

If sinA=1/2 , show that 3 cos A - 4 cos^(3) A= 0

If the equation x^(3) +px +q =0 has three real roots then show that 4p^(3)+ 27q^(2) lt 0 .

If A=[{:(1,0,-1),(2,1,3),(0,1,1):}] , then verify that A^(2)+A=A(A+I) where I is 3xx3 unit matrix.

If A=[{:(1,0,2),(0,2,1),(2,0,3):}] then , prove that A^(3)-6A^(2)+7A+2I=O .

Find A^(-1)" if "A=[{:(0,1,1),(1,0,1),(1,1,0):}] and show that A^(-1)=(A^2-3I)/2