Let A = [ * 20 c 1&2 3&4 ] and B = [ * 20 c a&0 0&b ] ;,a,b N the… - Vidyadip

MCQ

Let $A = \left[ {\begin{array}{*{20}{c}}1&2\\3&4\end{array}} \right]$ and $B = \left[ {\begin{array}{*{20}{c}}a&0\\0&b\end{array}} \right]\;,a,b \in N$ then

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 $AB = BA$
✓
there exist infinitely many $B's$ such that $AB = BA$

✓

Answer

Correct option: D.

there exist infinitely many $B's$ such that $AB = BA$

d
$A=\left[\begin{array}{ll}{1} & {2} \\ {3} & {4}\end{array}\right] \quad $ $B=\left[\begin{array}{ll}{a} & {0} \\ {0} & {b}\end{array}\right]$

$A B=\left[\begin{array}{ll}{a} & {2 b} \\ {3 a} & {4 b}\end{array}\right]$

$B A=\left[\begin{array}{ll}{a} & {0} \\ {0} & {b}\end{array}\right]\left[\begin{array}{ll}{1} & {2} \\ {3} & {4}\end{array}\right]$$=\left[\begin{array}{ll}{a} & {2 a} \\ {3 b} & {4 b}\end{array}\right]$

Hence, $A B=B A$ only when $a=b$

$\therefore$ There can be infinitely many $B^{\prime} s$

for which $A B=B A$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 3 and 4 . determinant and metrices→3 and 4 . determinant and metrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate : $\int \frac{d x}{\sqrt{x^2-3 x+2}}$

If the set of all values of $''a''$ is $\left[ {\alpha ,\beta } \right] \cup \left[ {\gamma ,\delta } \right]$ for which $\begin{gathered}
f\left( x \right) = \left\{ \begin{gathered}
3x + \left| {{a^2} - 4} \right|;a \leqslant x < 1 \hfill \\
5 - {x^2}\,\,\,\,\,\,\,\,;x \geqslant 1 \hfill \\
\end{gathered} \right. \hfill \\
\hfill \\
\end{gathered}$ has largest value at $x$ = $1$, then $\left( {\alpha + \beta + \gamma + \delta } \right)$ is equal to

Let $\text{f}:\text{R}-\Big\{\frac{3}{5}\Big\}\rightarrow\ \text{R}$ be defined by $\text{f(x)}=\frac{3\text{x}+2}{5\text{x}-3}.$ Then,

f^-1(x) = f(x)
f^-1(x) = -f(x)
fof(x) = -x
$\text{f}^{-1}(\text{x})=\frac{1}{19}\text{f(x)}$

If $\vec{\text{a}}$ and $\vec{\text{b}}$ be two unit vectors and $\theta$ the angle between them, than $\vec{\text{a}}+\vec{\text{b}}$ is a unit vector if $\theta=$

$\frac{\pi}{4}$
$\frac{\pi}{3}$
$\frac{\pi}{2}$
$\frac{2\pi}{3}$

Out of 30 consecutive integers, 2 are chosen at random. The probability that their sum is odd, is

Which of the following represents direction cosines of the line:

$0,\frac{1}{\sqrt{2}},\frac{1}{2}$
$0,\frac{-\sqrt{3}}{2},\frac{1}{\sqrt{2}}$
$0,\frac{\sqrt{3}}{2},\frac{1}{2}$
$\frac{1}{2},\frac{1}{2},\frac{1}{2}$

Let $f: R \rightarrow R$ be defined as $f(x)=x-1$ and $g: R -\{1,-1\} \rightarrow R$ be defined as $g(x)=\frac{x^{2}}{x^{2}-1}$. Then the function fog is

If function $f(x)=\left\{\begin{array}{c}\frac{x^2-16}{x-4}, x \neq 4 \\ k, x=4\end{array}\right.$, is continuous at $x=4$, then value of $k$ is :

The area bounded by the lines y = |x – 2|, x = 1, x = 3 and the x- axis is:

1 sq. unit
2 sq. units
3 sq. units
4 sq. units

The integral value $\int_{ - 2}^0 {\left[ {{x^3} + 3{x^2} + 3x + 3 + (x + 1)\cos (x + 1)} \right]\;dx} $ is