If for the matrix A , A^3 = I, then A^ - 1 = - Vidyadip

MCQ

If for the matrix $ A$ , ${A^3} = I$, then ${A^{ - 1}} = $

✓
${A^2}$
B
${A^3}$
C
$A$
D
None of these

✓

Answer

Correct option: A.

${A^2}$

a
(a)${A^{ - 1}} = {A^2}$, because ${A^3} = I$.

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

For the function $f(x) = {e^x},a = 0,b = 1$, the value of $ c$ in mean value theorem will be

$\int_{\,8}^{\,15} {\frac{{dx}}{{(x - 3)\sqrt {x + 1} }} = } $

The probability of obtaining an even prime number on each die, when a pair of dice is rolled is

0
$\frac{1}{3}$
$\frac{1}{12}$
$\frac{1}{36}$

If $f(x) = \frac{x}{{1 + x}}$, then ${f^{ - 1}}(x)$ is equal to

If the line $x=\alpha$ divides the area of region $R=\left\{(x, y) \in \mathrm{R}^2: x^3 \leq y \leq x, 0 \leq x \leq 1\right\}$ into two equal parts, then $[A]$ $0<\alpha \leq \frac{1}{2}$ $[B]$ $\frac{1}{2}<\alpha<1$ $[C]$ $2 \alpha^4-4 \alpha^2+1=0$ $[D]$ $\alpha^4+4 \alpha^2-1=0$

If A = [a_ij] is a square matrix of even order such that a_ij = i² - j², then

A is a skew-symmetric matrix and |A| = 0
A is symmetric matrix and |A| is a square
A is symmetric matrix and |A| = 0
None of these.

$\int_{}^{} {\frac{{{e^x}(x + 1)}}{{{{\cos }^2}(x{e^x})}}dx = } $

$\int\frac{\sin\text{x}}{3+4\cos^2\text{x}}\text{ dx}=$

$\log(3+4\cos^2\text{x})+\text{C}$
$\frac{1}{2\sqrt{3}}\tan^{-1}\Big(\frac{\cos\text{x}}{\sqrt{3}}\Big)+\text{C}$
$-\frac{1}{2\sqrt{3}}\tan^{-1}\Big(\frac{2\cos\text{x}}{\sqrt{3}}\Big)+\text{C}$
$\frac{1}{2\sqrt{3}}\tan^{-1}\Big(\frac{2\cos\text{x}}{\sqrt{3}}\Big)+\text{C}$

Cosine of the angle between two diagonals of acube is equal to:

$\frac{2}{\sqrt{6}}$
$\frac{1}{3}$
$\frac{1}{2}$
None of these

$\int_{}^{} {\sqrt {2 + \sin 3x} \;.\;\cos 3x\;dx = } $