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

Examine the consistency of the system of equations:
x + 2y = 2
2x + 3y = 3
→
Evaluate the following integrals:
$\int(\sec^2\text{x}+\text{cosec}^2\text{x})\text{dx}$
→
Find the maximum and minimum value, f(x) = (2x - 1)2 + 3
→
Find the value of $\int \frac{\sin 2 x d x}{(a-b \cos x)^2}$.
→
If $\pi\leq\text{x}\leq3\pi$ and $\text{y}=\cos^{-1}(\cos\text{x}),$ find $\frac{\text{dy}}{\text{dx}}.$
→
Find $\frac{dy}{dx}$ if sin2 x + cos2 y = 1
→
Verify that the function $x y=a e^{x}+b e^{-x}+x^{2}$ (implicit or explicit) is a solution of the differential equation $x \frac{d^{2} y}{d x^{2}}+2 \frac{d y}{d x}-x y+x^{2}-2=0$ 
→
Find the value of x, if:
$\begin{vmatrix}\text{x}+1&\text{x}-1\\\text{x}-3&\text{x}+2\end{vmatrix}=\begin{vmatrix}4&-1\\1&3\end{vmatrix}$
→
Given two independent events A and B such that P(A) = 0.3 and P(B) = 0.6. Find
$\text{P}(\text{A}\cup\text{B})$
→
If $A=\left[\begin{array}{ll}2 & 5 \\ 3 & 8\end{array}\right]$ then find $A ^{-1}$.
→