Choose the correct option about the matrices given below ( aligned & A= [ array ccc 4 & 4 & 0 - 4 & 4 & 0 0 & 0 & 1 array ] & B= [ array ccc 1 & 0 & 0 0 & 3 & 3 0 & - 3 & 3 array ] & C= [ array ccc 6 & 0 & 6 0 & 1 & 0 - 6 & 6 & 0 array ] aligned ) (D= [ array ccc 2 & 2 & 0 - 2 & 2 & 0 0 & 0 & 1 array ] )

Step-by-step solution

Given matrix ( aligned & A= [ array ccc 4 & 4 & 0 - 4 & 4 & 0 0 & 0 & 1 array ] & A^2= [ array ccc 2 & 2 & 0 - 2 & 2 & 0 0 & 0 & 1 array ] aligned ) ( array ll & A^2=D= [ array ccc 2 & 2 & 0 - 2 & 2 & 0 0 & 0 & 1 array ]= [ array ccc 0 & 1 & 0 -1 & 0 & 0 0 & 0 & 1 array ] & A^4= [ array ccc -1 & 0 & 0 0 & -1 & 0 0 & 0 & 1 array ]=D^2 A^8= [ array lll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ] & A²⁰²⁰= (A⁵⁰⁵ )^4= ( (A^8 )⁶³ A )^4= (I⁶³ A )^4=A^4 I array ) Similarly, (D^4=I ), so (D²⁰¹⁹ I ) Now, (B= [ array ccc 1 & 0 & 0