If the matrix A= (1 Tanx -Tanx 1) Show that A Transpose x A inverse=(Cos2x -Sin2x Sin2x Cos2x)

Question

If the matrix A= (1 Tanx -Tanx 1) Show that A Transpose x A
inverse=(Cos2x -Sin2x Sin2x Cos2x) ​

Ashish Shukla · Accepted Answer

Dear Student,
A=1tanx-tanx1AT=1-tanxtanx1A=1+tan2x=sec2x
A-1=1A1-tanxtanx1=1sec2x1-tanxtanx1AT×A-1=1sec2x1-tanxtanx1×1-tanxtanx1=1sec2x1-tan2x-2tanx2tanx1-tan2x=1-tan2xsec2x-2tanxsec2x2tanxsec2x1-tan2xsec2x=cos2x-sin2xcos2xsec2x-2tanxsec2x2tanxsec2xcos2x-sin2xcos2xsec2x=cos2x-2sinxcosx2sinxcosxcos2x=cos2x-sin2xsin2xcos2x=RHS

If the matrix A= (1 Tanx -Tanx 1) Show that A Transpose x A inverse=(Cos2x -Sin2x Sin2x Cos2x) ​