If A= [ cc 2 & 2 -3 & 2 ], B= [ cc 0 & -1 1 & 0 ] then (B^ -1 A^ … - Vidyadip

MCQ

If $A=\left[\begin{array}{cc}2 & 2 \\ -3 & 2\end{array}\right], B=\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]$ then $\left(B^{-1} A^{-1}\right)^{-1}=$

✓
$\left[\begin{array}{cc}2 & -2 \\ 2 & 3\end{array}\right]$
B
$\left[\begin{array}{cc}2 & 2 \\ -2 & 3\end{array}\right]$
C
$\left[\begin{array}{cc}2 & -3 \\ 2 & 2\end{array}\right]$
D
$\left[\begin{array}{cc}1 & -1 \\ -2 & 3\end{array}\right]$

✓

Answer

Correct option: A.

$\left[\begin{array}{cc}2 & -2 \\ 2 & 3\end{array}\right]$

(a) : $A=\left[\begin{array}{cc}2 & 2 \\ -3 & 2\end{array}\right], B=\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]$
$\begin{array}{l}|A|=4+6=10 \neq 0 \text { and }|B|=0+1=1 \neq 0 \\ \therefore \quad A^{-1}, B^{-1} \text { exists } \\ \text { So, }\left(B^{-1} A^{-1}\right)^{-1}=\left(A^{-1}\right)^{-1}\left(B^{-1}\right)^{-1}=A B \\ =\left[\begin{array}{cc}2 & 2 \\ -3 & 2\end{array}\right]\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]=\left[\begin{array}{cc}0+2 & -2+0 \\ 0+2 & 3+0\end{array}\right]=\left[\begin{array}{cc}2 & -2 \\ 2 & 3\end{array}\right]\end{array}$

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 Determinants→Determinants — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The minimum value of $f(a) = (2{a^2} - 3) + 3(3 - a) + 4$ is

If the function $f(x)=\left\{\begin{array}{l}\frac{\left(e^{k x}-1\right) \tan k x}{4 x^2}, x \neq 0 \\ 16, x=0\end{array}\right.$ is continuous at $x=0$, then $k=$

The area of the region bounded by the and the lines x = 2 and x = 3.

$\frac{7}{2}\text{sq}.\text{units}$
$\frac{9}{2}\text{sq}.\text{units}$
$\frac{11}{2}\text{sq}.\text{units}$
$\frac{13}{2}\text{sq}.\text{units}$

The scalar projection of the vector $3 \hat{ i }-\hat{ j }-2 \hat{ k }$ on the vector $\hat{i}+2 \hat{j}-3 \hat{k}$ is

${d \over {dx}}{\cos ^{ - 1}}{{x - {x^{ - 1}}} \over {x + {x^{ - 1}}}} =$

If $x = \exp \left\{ {{{\tan }^{ - 1}}\left( {{{y - {x^2}} \over {{x^2}}}} \right)} \right\}\,\,$, then ${{dy} \over {dx}}$ equals

If $x + \frac{1}{x} = 2$, the principal value of ${\sin ^{ - 1}}$ $x$ is

The area of the region bounded by the curve x = 2y + 3 and lines y = 1 and y = –1 is:

$4\text{ sq.}\text{ units}$
$\frac{2}{3}\text{ sq.}\text{ units}$
$6\text{ sq.}\text{ units}$
$8\text{ sq.}\text{ units}$

For the system of linear equations :

$x-2 y=1, x-y+k z=-2, k y+4 z=6, k \in R$

consider the following statements :

$(A)$ The system has unique solution if $k \neq 2$, $k \neq-2$

$(B)$ The system has unique solution if $k =-2$.

$(C)$ The system has unique solution if $k =2$.

$(D)$ The system has no-solution if $k =2$.

$(E)$ The system has infinite number of solutions if $k \neq-2$

Which of the following statements are correct?

$\int \frac{d x}{x^2-9}$ equal to :