Download App

Adjoint and Inverse of a Matrix — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSAdjoint and Inverse of a Matrix2 Marks
Question
Let $A$ be a square matrix such that $A^2 - A + I = 0,$ then write $A^{-1}$ interms of $A.$
✓

Answer

$A^2 - A + I = 0$
$Px-$multiplying with $A^{-1},$
$(A^{-1} A) - (A^{-1} A) + A^{-1}I = 0$
$IA - I + A^{-1} = 0$
$A^{-1} = I - A$
Hence $,A^{-1} = I - A$

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 "2 Marks Questions" from Adjoint and Inverse of a Matrix→Adjoint and Inverse of a Matrix — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Integrate the function: $\frac{1}{{x + x\log x}}$
→
Let $R = \{(x, y): |x^2 - y^2| < 1\}$ be a relation on set $A = \{1, 2, 3, 4, 5\}.$ Write $R$ as a set of ordered pairs.
→
If $\begin{bmatrix}\text{xy}&4\\\text{z}+6&\text{x}+\text{y}\end{bmatrix}=\begin{bmatrix}8&\text{w}\\0&6\end{bmatrix},$ then find the values of $x, y, z$ and $w.$
→
Determine the direction cosines of the normal to the plane and the distance from the origin.
z = 2
→
If A = {3, 5, 7} and B = {2, 4, 9} and R is a relation given by "is less than", write R as a set ordered pairs.
→
If $\vec{\text{a}},\ \vec{\text{b}},\ \vec{\text{c}}$ are non-coplanar vectors, prove that the given vectors are non-coplanar:
$2\vec{\text{a}}-\vec{\text{b}}+3\vec{\text{c}},\ \vec{\text{a}}+\vec{\text{b}}-2\vec{\text{c}}$ and $\vec{\text{a}}+\vec{\text{b}}-3\vec{\text{c}}$
→
Find that point on curve $y=x^2-2 x+3$, the tangent drawn on that is parallel to line $2 \mathrm{x}-\mathrm{y}+9=0$.
→
Find an anti derivative (or integral) of function by the method of inspection cos 3x.
→
Find the length of the perpendicular drawn from the origin to the plane $2x − 3y + 6z + 21 = 0.$
→
If $\vec{\text{a}}$ and $\vec{\text{b}}$ are two vectors such that $\vec{\text{a}}.\vec{\text{b}}=6,|\vec{\text{a}}|=3$ and $\big|\vec{\text{b}}\big|=4.$ write the projection of $\vec{\text{a}}$ on $\vec{\text{b}}.$
→