If A - begin bmatrix 182 13 4lend bmatrix - B - bmatrix a 0 10 blend bmatrix- a- b - N- then number of matrix - B - such that A B-B A areA- 1B- 0C- infiniteD- finitely many

The correct option is C infinite AB=[ a amp; 2b; 3a amp; 4b ],BA=[ a amp; 2a; 3b amp; 4b ] AB = BA ⇒ a = b ...

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Byju's Answer

Standard XII

Mathematics

Adjoint of a Matrix

If A = begin ...

Question

If $A = [\begin{matrix} 1 & 2 3 & 4 \end{matrix}], B = [\begin{matrix} a & 0 0 & b \end{matrix}]$ ,a,b $ϵ$ N, then number of matrix ‘B’ such that AB = BA are

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finitely many

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infinite

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Solution

The correct option is C infinite
$A B = [\begin{matrix} a & 2 b 3 a & 4 b \end{matrix}], B A = [\begin{matrix} a & 2 a 3 b & 4 b \end{matrix}]$
AB = BA $\Rightarrow$ a = b

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Similar questions

Q. If A=

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

then number of matrix ‘B’ such that AB = BA are

Q. Let

A = [\begin{matrix} 1 & 2 3 & 4 \end{matrix}]

and

B = [\begin{matrix} a & b c & d \end{matrix}]

are two matrices such that AB = BA and

c \neq 0

, then value of

\frac{a - d}{3 b - c}

is :

Let $A = [\begin{matrix} 1 & 2 3 & 4 \end{matrix}]$ and $B = A = [\begin{matrix} a & b c & d \end{matrix}]$ are two matrices such that AB = BA and $c \neq 0$ , then value of $\frac{a - d}{3 b - c}$ is :

Q. 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

Q. Let

A = [\begin{matrix} 1 & 2 3 & 4 \end{matrix}]

and

B = [\begin{matrix} a & b c & d \end{matrix}]

are two matrices such that AB = BA and

c \neq 0

, then value of

\frac{a - d}{3 b - c}

is :

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If A=[1234],B=[a00b],a,b ϵ N, then number of matrix ‘B’ such that AB = BA are

The correct option is C infinite AB=[a2b3a4b],BA=[a2a3b4b] AB = BA ⇒ a = b

If $A = [\begin{matrix} 1 & 2 3 & 4 \end{matrix}], B = [\begin{matrix} a & 0 0 & b \end{matrix}]$ ,a,b $ϵ$ N, then number of matrix ‘B’ such that AB = BA are

The correct option is C infinite
$A B = [\begin{matrix} a & 2 b 3 a & 4 b \end{matrix}], B A = [\begin{matrix} a & 2 a 3 b & 4 b \end{matrix}]$
AB = BA $\Rightarrow$ a = b