If A is idemponent matrix, then find the value of  (A+I)n, ∀n∈N Where I is the identity matrix having the same order of A.

# If $A$ is idemponent matrix, then find the value of  ${\left(A+I\right)}^{n}$ Where $I$ is the identity matrix having the same order of $A$.

1. A

$I+\left({2}^{n}-1\right)A$

2. B

$I\mathit{-}\left({2}^{n}-1\right)A$

3. C

$\mathit{3}I+\left({2}^{n}-1\right)A$

4. D

$\mathit{4}I+\left({2}^{n}-1\right)A$

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

### Solution:

is idemponent matrix

,

similarly

Now, ${\left(A+I\right)}^{n}={\left(I+A\right)}^{n}$

Hence, .

## Related content

 Area of Square Area of Isosceles Triangle Pythagoras Theorem Triangle Formulae Perimeter of Triangle Formula Area Formulae Volume of Cone Formula Matrices and Determinants_mathematics Critical Points Solved Examples Type of relations_mathematics  +91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)