Download App

MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES2 Marks
Question
Let A and B be square matrices of the same order. Does (A + B)2 = A2 + 2AB + B2 hold? If not, why?
✓

Answer

LHS = (A + B)2
= (A + B)(A + B)
= A(A + B) + B(A + B)
= A2 + AB + BA + B2
We know that a matrix does not have commutative property. So,
AB ≠ BA
Thus,
(A + B)2 ≠ A2 + 2AB + B2

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" from MATRICES→MATRICES — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Write the domain of the real function $\text{f(x)}=\sqrt{\text{x}-[\text{x}]}.$
→
Write the coordinates of the projection of point P(x, y, z) on XOZ-plane.
→
Find the value of the determinant $\begin{vmatrix}243&156&300\\81&52&100\\-3&0&4\end{vmatrix}$
→
Integrate the function in Exercise:

$\frac{2+\sin2\text{x}}{1+\cos2\text{x}}\text{e}^{\text{x}}$

→
Evaluate:
$\sin\Big(\tan^{-1}\text{x}+\tan^{-1}\frac{1}{\text{x}}\Big)\text{ for }\text{x}<0$
→
Evaluate the following integrals:
$\int\Big(\frac{\text{m}}{\text{x}}+\frac{\text{x}}{\text{m}}+\text{m}^\text{x}+\text{x}^\text{m}+\text{mx}\Big)\text{dx}$
→
Five cards are drawn successively with replacement from a well-shuffled pack of 52 cards. What is the probability that
none is a spade?
→
Let A = [aij] be a square matrix of order 3 × 3 and Cij denote cofactor of aij in A. if |A| = 5, write the value of a13C13 + a23C23 + a33C33.
→
Find the value of x for which $\text{x}\big(\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}\big)$ is a unit vector.
→
Find the area of the parallelogram whose adjacent sides are determined by the vectors $\vec{a}=\hat{i}-\hat{j}+3\hat{k}\ \text{and}\ \vec{b}=2\hat{i}-7\hat{j}+\hat{k}.$
→