If A= [ ll 2 & -3 5 & -7 ], then A-A^ -1 = - Vidyadip

MCQ

If $A=\left[\begin{array}{ll}2 & -3 \\ 5 & -7\end{array}\right]$, then $A-A^{-1}=$

A
$\left[\begin{array}{cc}-5 & 0 \\ 0 & -5\end{array}\right]$
B
$3\left[\begin{array}{cc}3 & 2 \\ 10 & 3\end{array}\right]$
✓
$3\left[\begin{array}{cc}3 & -2 \\ \frac{10}{3} & -3\end{array}\right]$
D
$5\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]$

✓

Answer

Correct option: C.

$3\left[\begin{array}{cc}3 & -2 \\ \frac{10}{3} & -3\end{array}\right]$

(c) : Given, $A=\left[\begin{array}{ll}2 & -3 \\ 5 & -7\end{array}\right]$, then $A^{-1}=\left[\begin{array}{ll}-7 & 3 \\ -5 & 2\end{array}\right]$
Now, $A-A^{-1}=\left[\begin{array}{ll}2 & -3 \\ 5 & -7\end{array}\right]-\left[\begin{array}{ll}-7 & 3 \\ -5 & 2\end{array}\right]$
$
=\left[\begin{array}{cc}
9 & -6 \\
10 & -9
\end{array}\right]=3\left[\begin{array}{cc}
3 & -2 \\
10 / 3 & -3
\end{array}\right]
$

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 "MCQ" from Matrics→Matrics — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

If $\quad \bar{a}=2 \hat{i}-3 \hat{j}+5 \hat{k}, \bar{b}=3 \hat{i}-4 \hat{j}+5 \hat{k} \quad$ and $\overline{ c }=5 \hat{ i }-3 \hat{ j }-2 \hat{ k }$, then the volume of the parallelopiped with coterminous edges $\overline{ a }+\overline{ b }, \overline{ b }+\overline{ c }, \overline{ c }+\overline{ a }$ is

If the vectors $3\hat{\text{i}}+\lambda\hat{\text{j}}+\hat{\text{k}}$ and $2\hat{\text{i}}-\hat{\text{j}}+8\hat{\text{k}}$ are perpendicular, then $\lambda$ is equal to:

If $A$ is an invertible matrix of order $3,$ then which of the following is not true:

The inverse of $A=\left[\begin{array}{lll}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{array}\right]$

If $A=\left[\begin{array}{ccc}1 & 0 & 0 \\ 3 & 3 & 0 \\ 5 & 2 & -1\end{array}\right]$, then $\operatorname{adj} A$ is

If n is any integer, then $\int_0^\pi e ^{\cos ^2 x} \cos ^3(2 n +1) x d x=$

If the angles of a triangle ABC be in A.P., then

$\tan ^{-1}\left(\tan \frac{7 \pi}{6}\right)=$

The general solution of the differential equation of all circles having centre at $A(-1,2)$ is

$\int_0^4 \frac{1}{\sqrt{4 x-x^2}} d x=$