Download App

Matrics — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsMatrics2 Marks
MCQ
If $A ^2- A + I =0$, then $A ^{-1}=$
  • A
    $A^{-2}$
  • B
    $A + I$
  • ✓
    $I - A$
  • D
    $A - I$
✓

Answer

Correct option: C.
$I - A$
(C) $A^2-A+I=0$
$\Rightarrow A \cdot A - A + I =0$
$\Rightarrow A ^{-1} \cdot A \cdot A - A ^{-1} \cdot A+ A ^{-1} \cdot I =0$
$\Rightarrow A - I + A ^{-1}=0$
$\Rightarrow A ^{-1}= I - A$

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 "MCQ" from Matrics→Matrics — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

The area bounded by the straight lines $x=0$, $x=2$ and the curves $y=2^x, y=2 x-x^2$ is
→
The primitive of the function $\text{f(x)}=\Big(1-\frac{1}{\text{x}^2}\Big)\text{a}^{\text{x}+\frac{1}{\text{x}}},\text{ a}>0$ is:
→
For $0 \leq x \leq \pi$, the area bounded by $y=x$ an $y=x+\sin x$, is
→
If $\text{y}=\frac{1}{1+\text{x}^{\text{a}-\text{b}}+\text{x}^{\text{c}-\text{b}}}+\frac{1}{1+\text{x}^{\text{b}-\text{c}}+\text{x}^{\text{a}-\text{c}}}+\frac{1}{1+\text{x}^{\text{b}-\text{a}}+\text{x}^{\text{c}-\text{a}}},$ then $\frac{\text{dy}}{\text{dx}}$ is equal to:
→
Function $\text{f}(\text{x})=\cos\text{x}-2\lambda\text{x}$ is monotonic decreasing when:
→
If $\int\frac{\sin^8\text{x}-\cos^8\text{x}}{1-2\sin^2\text{x}\cos^2\text{x}}\text{ dx}=\text{a}\sin2\text{x}+\text{C},$ then $a =$
→
$\int\frac{\text{x}+3}{(\text{x}+4)^2}\text{e}^{\text{x}}\text{ dx}=$
→
Bernoulli distribution is a particular case of binomial distribution if $n=$____
→
If $A$ is an invertible matrix of order $3,$ then which of the following is not true:
→
If the line $\overline{ r }=\hat{ i }+\lambda(2 \hat{ i }- m \hat{ j }-3 \hat{ k })$ is parallel to the plane $\overline{ r } \cdot( m \hat{ i }+3 \hat{ j }+\hat{ k })=0$, then m is equal to
→