Download App

Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
MCQ
If $A^5 = 0$ Such that $\text{A}^{\text{n}}\neq\text{I}$ for $1\leq\text{n}\leq4,$ then $(\text{I}-\text{A})^{-1}$ equals :
  • A
    $A^4$
  • B
    $A^3$
  • C
    $I + A$
  • ✓
    None of these.
✓

Answer

Correct option: D.
None of these.
$A^5=0$
Using $a^5-b^5=(a-b)\left(a^4+a^3 b+a^2 b^2+a b^3+b^4\right)$
$I-A^5=(I-A)\left(I+A+A^2+A^3+A^4\right)$
$I=(I-A)\left(I+A+A^2+A^3+A^4\right)$
$(I-A)^{-1} I=(I-A)^{-1}(I-A)\left(I+A+A^2+A^3+A^4\right)$
$(I-A)-1=I+A+A^2+A^3+A^4$

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 Determinants→Determinants — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The function $\text{f(x)}=\sin^{-1}(\cos\text{x})$ is:
→
The value of $\int \limits_{-2012}^{2012}\left(\sin \left(x^3\right)+x^5+1\right) d x$ is
→
If the function $f:(-\infty,-1] \rightarrow(a, b]$ defined by $f(x)=e^{x^3-3 x+1}$ is one-one and onto, then the distance of the point $\mathrm{P}(2 \mathrm{~b}+4, \mathrm{a}+2)$ from the line $x+e^{-3} y=4$ is :
→
The vector equation of the line passing through the point (-1, 5, 4) and perpendicular to the plane z = 0 is:
→
If  $ a, b, c, d$  are coplanar vectors, then $(a \times b) \times (c \times d) = $
→
Statement $1$ : A function $f:R \to R$ is continuous at $x_0$ if and only if $\mathop {\lim }\limits_{x \to {x_0}} \,f\left( x \right)$ exists and $\mathop {\lim }\limits_{x \to {x_0}} \,f\left( x \right) = f\left( {{x_0}} \right)$

Statement $2$ :  A function $f : R \to R$ is discontinuous at $x_0$ if and only if, $\mathop {\lim }\limits_{x \to {x_0}} \,f\left( x \right)$ exists and $\mathop {\lim }\limits_{x \to {x_0}} \,f\left( x \right) \ne f\left( {{x_0}} \right)$

→
Define a function $f(x)=\frac{16 x^2-96 x+153}{x-3}$ for all real $x \neq 3$. The least positive value of $f(x)$ is
→
The value of the integral $\int_{0}^{\frac{\pi}{2}} 60 \frac{\sin (6 x)}{\sin x} d x$ is equal to.
→
If the events $A$ and $B$ are independent, then $\text{P}(\text{A}\cap\text{B})$ is equal to,
→
Which of the following function $(s)$ is/are Transcidental?
→