Let A- 1 2- 3 4 - and B- a 0- 0 b - a-b - N-Then

The correct option is D there exist infinitely many B's such that AB = BA. A=[ 1 amp; 2; 3 amp; 4 ] and B=[ a amp; 0; 0 amp ...

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Byju's Answer

Standard XII

Mathematics

Adjoint of a Matrix

Let A=[ 1 2...

Question

Let $A = (\begin{matrix} 1 & 2 3 & 4 \end{matrix})$ and $B = (\begin{matrix} a & 0 0 & b \end{matrix}) a, b ϵ N .$ Then

there cannot exist any B such that

A B = B A

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there exist more than one but finite number of B's such that

A B = B A

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there exists exactly One B such that

A B = B A

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there exist infinitely many B's such that

A B = B A .

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Solution

The correct option is D there exist infinitely many B's such that $A B = B A .$
$A = [\begin{matrix} 1 & 2 3 & 4 \end{matrix}]$ and $B = [\begin{matrix} a & 0 0 & b \end{matrix}]$
$A B = [\begin{matrix} a & 2 b 3 a & 4 b \end{matrix}]$
$B A = [\begin{matrix} a & 2 a 3 b & 4 b \end{matrix}]$
$A B = B A \Rightarrow a = b$
$∴$ there exist infinitely many $B^{'} s$ such that $A B = B A$ .

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Let A=(1234) and B=(a00b)a,bϵN.Then

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