Question
If $A^3=O$, then $A^2+A+I=$

Answer

(b) $: I-A^3=I \Rightarrow(I-A)\left(I+A+A^2\right)=I$
$\therefore \quad I+A+A^2=(I-A)^{-1}$.

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

Similar questions

Direction cosines of ray from P(1, −2, 4) to Q(−1, 1, −2) are:
  1. −2, 3, −6
  2. 2, −3, 6
  3. 2, 3, 6
  4. $\frac{-2}{7},\frac{3}{7},\frac{-6}{7}$
If $A=\left[\begin{array}{ccc}3 & -1 & 2 \\ 2 & 1 & 3 \\ 1 & -3 & K\end{array}\right]$ is non-invertible matrix, then value of K :
If matrix A and B are of the order $m \times n$ and $n \times p$ respectively, then order of AB is
The distance of the line $\vec{\text{r}}=2\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}+\lambda(\hat{\text{i}}-\hat{\text{j}}+4\hat{\text{k}})$ from the plane $\vec{\text{r}}.(\hat{\text{i}}+5\hat{\text{j}}+\hat{\text{k}})=5$ is:
  1. $\frac{5}{3\sqrt{3}}$
  2. $\frac{10}{3\sqrt{3}}$
  3. $\frac{25}{3\sqrt{3}}$
  4. $\text{None of these}$
The value of $\int\frac{\text{d}(\text{x}^2+1)}{\sqrt{\text{x}^2+2}}$ is:
  1. $2\sqrt{\text{x}^2+2}+\text{c}$
  2. $\sqrt{\text{x}^2+2}+\text{c}$
  3. $\text{x}\sqrt{\text{x}^2+2}+\text{c}$
  4. ${4}\sqrt{\text{x}^2+2}+\text{c}$
In the set Z of all integers, which of the following relation R is not an equivalence relation?
  1. xRy : if $\text{x}\leq\text{y}$
  2. xRy : if x = y
  3. xRy : if x - y is an even integer
  4. xRy : if $\text{x}\equiv\text{y}\ (\text{mod 3})$
If the position vectors of the points A and B are $\vec{a}$ and $\vec{b}$ respectively, then the position vector of the mid-point of the line $A B$ will be :
If A is a singular matrix, then adj A is:
  1. Non-singular.
  2. Singular.
  3. Symmetric.
  4. Not defined.
If $\text{f(x)}=\begin{cases}\frac{|\text{x}+2|}{\tan^{-1}(\text{x}+2)}, & \text{x}\neq-2\\2, & \text{x}=-2\end{cases},$ then f(x) is:
  1. Continuous at x = -2
  2. Not continuous at x = -2
  3. Diffrentiable at x = -2
  4. Continuous but nit derivable at x = -2
If $A$ and $B$ are two matrices of same order, then $A + B$ is equal to: