Let A be a matrix such that A . [ array ll 1 & 2 0 & 3 array ] is a scalar matrix and |3 A|=108 . Then A^2 equals

Step-by-step solution

A. [ array ll 1 & 2 0 & 3 array ] is a scalar matrix and |3 ~A |=108 suppose the scalar matrix is [ array ll k & 0 0 & k array ] aligned & A [ array ll 1 & 2 0 & 3 array ]= [ array ll k & 0 0 & k array ] & A= [ array ll k & 0 0 & k array ] [ array ll 1 & 2 0 & 3 array ]⁻¹ & [ A B=C A B B⁻¹=C B⁻¹ A=C B⁻¹ ] & A= 1 3 [ array ll k & 0 0 & k array ] [ array cc 3 & -2 0 & 1 array ] & A= [ array ll k & 0 0 & k array ] [ array cc 1 & - 2 3 0 & 1 3 array ] aligned A= [ array cc k & - 2 3 k 0 & k 3 array ] |3 ~A |=108 108= |