Q10 of 307 Page 6

If denote the direction cosines of three mutually perpendicular vectors in space, prove that AA^T = I, where

Given,

are direction cosines of three mutually perpendicular vectors

And given,

Hence,

If then verify that A^TA = I₂.

If verify that A^TA = I₂.

If prove that A – A^T is a skew-symmetric matrix.

If show that A – A^T is a skew-symmetric matrix.

If denote the direction cosines of three mutually perpendicular vectors in space, prove that AAT = I, where