If both A- I 2 and A+ I 2 are orthogonal matrix, then which of the following statements are incorrect? (where I is an identity matrix order same as that of A .)

Step-by-step solution

Given that both the matrices A- I 2 and A+ I 2 are orthogonal that means (A- I 2 ) (A^ - I 2 )=I ( . as .I^ =I )A A^ - A I 2 - A^ I 2 + I 4 =I ...(1) ( as I^2=I ) Also, (A+ I 2 ) (A+ I 2 )^ =I (A+ I 2 ) (A^ + I 2 )=IA A^ + A I 2 + A^ I 2 + I 4 =I ...(2) Subtracting eqn. (1) from eqn. (2), we get A I+A^ I=0 A=-A^ Hence, A is an skew-symmetric matrix Now, for order of matrix add eqn. (1) and eqn. (2), we get A A^ = 3 I 4 Hence, |A|^2 0 have this so even order.