AP EAMCET202017 Sep 2020Evening ShiftMathematicsMatricesActual
Let (M ) and (N ) be two matrices over (R ) of order 2. Then, (M N=N M ) if .......
Options
- AOne of (M ) and (N ) is a diagonal matrix
- BBoth (M ) and (N ) are diagonal matrices
- CBoth (M ) and (N ) are invertible matrices
- DNone of these options are true in general
Correct answer
B. Both (M ) and (N ) are diagonal matrices
Step-by-step solution
Let (M= ( array ll a & b c & d array ), N= ( array ll p & q r & s array ) ) Then, ( M N= ( array ll a p+b r & a q+b s p c+d r & c q+d s array ) ) and ( N M= ( array cc a p+q c & p b+q d a r+c s & b r+d s array ) ) Clearly, (M N=N M ) When, ( aligned & b r=0, q c=0 & p c=0, d r=0 & or, If b=c=q=r=0 aligned ) i.e., both (M ) and (N ) must be diagonal matrices.