Download App

MATRICES — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSMATRICES2 Marks
Question
Let $A$ and $B$ be square matrices of the same order. Does $(A + B)^2 = A^2 + 2AB + B^2$ hold? If not, why?
✓

Answer

$\text{LHS} = (A + B)^2$
$= (A + B)(A + B)$
$= A(A + B) + B(A + B)$
$= A^2 + AB + BA + B^2$
We know that a matrix does not have commutative property.
So, $AB \neq BA$
Thus, $(A + B)^2 \neq A^2 + 2AB + B^2$

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 MATRICES→MATRICES — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Evaluate the following:
$\cot^{-1}\Big\{\cot\Big(-\frac{8\pi}{3}\Big)\Big\}$
→
If f(x) = x + 1 then write the value of $\frac{\text{d}}{\text{dx}}\text{ fof }\text{(x)}.$
→
If $\text{y}=\sec^{-1}\Big(\frac{\text{x}+1}{\text{x}-1}\Big)+\sin^{-1}\Big(\frac{\text{x}-1}{\text{x}+1}\Big),$ then write the value of $\frac{\text{dy}}{\text{dx}}.$
→
If $A = [A_{ij}]$ is  $3 \times 3$ diaginal matrix such that $a_{11} = 1, a_{22} = 2, a_{33} = 3,$ then find $|A|.$
→
An insurance company insured $2000$ scooter drivers$, 4000$ car drivers and $6000$ truck drivers. The probability of an accidents are $0.01, 0.03$ and $0.15$ respectively. One of the insured persons meet with an accident. What is the probability that he is a scooter driver?
→
An urn contains 7 red and 4 blue balls. Two balls are drawn at random with replacement. Find the probability of getting,
2 Blue balls.
→
Find the principal value of the following:
$\cos^{-1}\Big(\sin\frac{4\pi}{3}\Big)$
→
If $C_{ij}$ is the cofactor of the element $a_{ij}$ of the matrix $\text{A}=\begin{bmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{bmatrix},$ then write the value of $a_{32}C_{32}.$
→
Write down a unit vector in $XY-$plane, making an angle of $30^\circ$ with the positive direction of $x-$axis.
→
Find the set values of $\text{cosec}^{-1}\Big(\frac{\sqrt3}{2}\Big)$
→