Let A = ( ll 2 & -2 1 & -1 ) and B = ( ll -1 & 2 -1 & 2 ). Then t… - Vidyadip

MCQ

Let $A =\left(\begin{array}{ll}2 & -2 \\ 1 & -1\end{array}\right)$ and $B =\left(\begin{array}{ll}-1 & 2 \\ -1 & 2\end{array}\right)$. Then the number of elements in the set $\left\{( n , m ): n , m \in\{1,2, \ldots . .10\}\right.$ and $\left.nA ^{ n }+ mB ^{ m }= I \right\}$ is

✓
$1$
B
$3$
C
$5$
D
$8$

✓

Answer

Correct option: A.

$1$

a
$A ^{2}= A$ and $B ^{2}= B$

Therefore equation $nA ^{ n }+ mB ^{ m }= I$ becomes $nA + mB = I$, which gives $m = n =1$

Only one set possible

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 STD 12 - 3 and 4 . determinant and metrices→STD 12 - 3 and 4 . determinant and metrices — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

For any two events $A$ and $B,$ if $P(\bar{A})=\frac{1}{2}, P(\bar{B})=\frac{2}{3}$ and $P(A \cap B)=\frac{1}{4}$, then $P(\bar{A} / \bar{B})$ equals:

$ABCDE$ is a pentagon. Forces $\overrightarrow {AB} ,\,\overrightarrow {AE} ,\,\overrightarrow {DC} ,\,\overrightarrow {ED} $ act at a point. Which force should be added to this system to make the resultant $ 2 \overrightarrow {AC} $

Perpendicular distance of the point $P (x, y, z)$ from $z$ axis is :

Let $\text{f(x)}=\frac{\alpha\text{x}}{\text{x}+1},\ \text{x}\neq-1.$ Then, for what value of $\alpha$ is $f(f(x)) = x?$

Let $A = \{1, 2, 3, …. n\}$ and $B = \{a, b\}$. Then the number of surjections from $A$ into $B$ is:

Choose the correct answer from the given four options.The order and degree of the differential equation $\Big[1+\Big(\frac{\text{dy}}{\text{dx}}\Big)^2\Big]=\frac{\text{d}^2\text{y}}{\text{d}\text{x}^2}$ are:

If the inverse trigonometric functions take principal values, then $\cos ^{-1}\left(\frac{3}{10} \cos \left(\tan ^{-1}\left(\frac{4}{3}\right)\right)+\frac{2}{5} \sin \left(\tan ^{-1}\left(\frac{4}{3}\right)\right)\right)$ is equal to

Let $*$ be a binary operation defined on $Q^+ $ by the rule $\text{a}*\text{b}=\frac{\text{ab}}3\forall\text{ a, b}\in \text{Q}^+$. The inverse of $4 * 6$ is:

Let $f(x)$ satisfy the requirement of lagranges mean value theorem in $[0,2]$ . If $f(x)=0$ ; $\left| {f'\left( x \right)} \right| \leqslant \frac{1}{2}$ for all $x \in \left[ {0,2} \right]$, then-

$\int\cos^{-1}(\frac{1}{\text{x}})\text{dx}$ equals: