Consider the matrix f(x)={[ able \cos x , - sin \;x , 0 ; sin \;x , \cos x , 0 ; 0 , 0 , 1]}.Given below are two statements :Statement I: f(-x) is the inverse of the matrix f(x).Statement II: f(x) f(y)=f(x+y).In the light of the above statements, choose the correct answer from the options given below [27-Jan-2024 Shift 1]

Question

Consider the matrix f(x)={[	able \cos x , - sin \;x , 0 ;  sin \;x , \cos x , 0 ; 0 , 0 , 1]}.Given below are two statements :Statement I: f(-x) is the inverse of the matrix f(x).Statement II: f(x) f(y)=f(x+y).In the light of the above statements, choose the correct answer from the options given below  [27-Jan-2024 Shift 1]

Examsnet · Accepted Answer

Correct Answer is :  Both Statement I and Statement II are true

cos‌x	−sin‌x	0
sin‌x	cos‌x	0
0	0	1

cos‌x	sin‌x	0
−sin‌x	cos‌x	0
0	0	1

cos‌y	−sin‌y	0
sin‌y	cos‌y	0
0	0	1

cos(x+y)	−sin‌(x+y)	0
sin‌(x+y)	cos(x+y)	0
0	0	1

JEE Main Math Class 12 Matrices Questions Part 2 Questions