A and B are n x n orthogonal matricies...show that

A(A^t+B^t)B=A+B

Where A^t and B^t are the transposes of A and B

Here is my working:

LHS= A(A^t+B^t)B

= (A*A^t+A*B^t)B

= (I+A*B^t)B

= IB+A*B^t*B

= B+A*I

= A+B

I know I have solved it correct and all..i jsut need some solid comfirmation..thats all thanks.