Let A = (1 2 3 4) and B = (a 0 0 b),a,b N. Then

(D) there exist infinitely many B' s such that AB=BA

(A) there cannot exist any B such that AB=BA

(B) there exist more then one but finite number of B' s such that AB=BA

(C) there exists exactly one B such that AB=BA

Matrices and Determinants: JEE Main 2006 Mathematics question

JEE Main 2006 · Annual, Paper 1 · Q4496

JEE Main 2006Annual, Paper 1MathematicsMediumMatrices and Determinants245× since 2002

Let

A = \left( {\matrix{ 1 & 2 \cr 3 & 4 \cr } } \right)

and

B = \left( {\matrix{ a & 0 \cr 0 & b \cr } } \right),a,b \in N.

Then

JEE Main 2006 · Annual, Paper 1 · Q4496

JEE Main 2006Annual, Paper 1MathematicsMediumMatrices and Determinants245× since 2002

Let

A = \left( {\matrix{ 1 & 2 \cr 3 & 4 \cr } } \right)

and

B = \left( {\matrix{ a & 0 \cr 0 & b \cr } } \right),a,b \in N.

Then