JEE Advanced2013MathematicsMatricesActual
For 3 x 3 matrices M and N, which of the following statement(s) is (are) not correct?
Options
- AN T MN is symmetric or skew-symmetric, according to as M is symmetric or skew-symmetric
- BMN - NM is skew symmetric for all symmetric matrices M and N
- CMN is symmetric for all symmetric matrices M and N
- Dadj(M) adj(N) = adj (MN) for all invertible matrices M and N
Correct answer
C. MN is symmetric for all symmetric matrices M and N
Step-by-step solution
N T MN T = N T M T N is symmetric if M is symmetric and skew-symmetric if M is skew-symmetric. MN - NM T = MN T - NM T = NM - MN = - MN - NM skew symmetric MN T = N T M T = NM ≠ MN hence not correct Standard result is adj MN = adj N adj M ≠ adj M adj N