CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Matrix $$\mathrm{A}$$ is such that $$\mathrm{A}^{2}=2\mathrm{A}-1$$ where 1 is the unit matrix Then for $$\mathrm{n}\geq 2,\ \mathrm{A}^{\mathrm{n}}=$$


A
nA(n1)I
loader
B
nAI
loader
C
2n+1A(n1)I
loader
D
2n+1A1
loader

Solution

The correct option is B $$nA-(n-1)I$$
$$A^2=2A-1$$
$$A^n=A^{n-2}A^2$$
$$=A^{n-2}(2A-1)$$
$$=2 A^{n-1}-A^{n-2}$$
$$A^2-2A+I=0$$
$$(A-I)=0$$
$$A=I$$
$$A^n=I$$
Put in all options only (A) comes out I

Maths

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image