QJEEM06Mae0f2: JEE Main 2006 Mathematics - Class 12 JEEM06Mae0f2 Solution: Let A = ( 1 2 3 4 ) and B = ( a 0 0 b ) , a , b ∈ N . Then

Question

Verified Solution • 2025–26 Session moderate

Let

A = (\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix})

and

B = (\begin{matrix} a & 0 \\ 0 & b \end{matrix}), a, b \in N .

Then

Accepted Answer

A = [\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}] B = [\begin{matrix} a & 0 \\ 0 & b \end{matrix}]

A B = [\begin{matrix} a & 2 b \\ 3 a & 4 b \end{matrix}]

B A = [\begin{matrix} a & 0 \\ 0 & b \end{matrix}] [\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}] = [\begin{matrix} a & 2 a \\ 3 b & 4 b \end{matrix}]

Hence,

A B = B A

only when

a = b

∴

There can be infinitely many

B^{'} s

for which

A B = B A

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