3 and 4 .Determinants and Matrices
medium

यदि $A = \left[ {\begin{array}{*{20}{c}}{\cos \alpha }&{ - \sin \alpha }\\{\sin \alpha }&{\cos \alpha }\end{array}} \right]$ और $B = \left[ {\begin{array}{*{20}{c}}{\cos \beta }&{ - \sin \beta }\\{\sin \beta }&{\cos \beta }\end{array}} \right]$, तो कौन सा सम्बन्ध सत्य है

A

${A^2} = {B^2}$

B

$A + B = B - A$

C

$AB = BA$

D

इनमें से कोई नहीं

Solution

(c) स्पष्टत:,  $AB = \left[ {\begin{array}{*{20}{c}}{\cos \alpha }&{ – \sin \alpha }\\{\sin \alpha }&{\cos \alpha }\end{array}} \right]\left[ {\begin{array}{*{20}{c}}{\cos \beta }&{ – \sin \beta }\\{\sin \beta }&{\cos \beta }\end{array}} \right]$

$ = \left[ {\begin{array}{*{20}{c}}{\cos (\alpha  + \beta )}&{ – \sin (\alpha  + \beta )}\\{\sin (\alpha  + \beta )}&{\cos (\alpha  + \beta )}\end{array}} \right] = BA$ (सत्यापित).

Standard 12
Mathematics

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