I need help with the following questions.

1) show that X & Y are orthogonal in Rn if and only if ||x+y|| = ||x-y||

2)let A be an n x n matrix, find a matrix A for which col A = null A

3) if A is m x n matrix and B is n x m matrix, show that AB = 0 if and only if col B is contained in null A

1) if x & y are orthogonal then x * y = 0 then what?

3) let y be a vector in of B [y1...yn]T then BX = 0 for all X in Rn

col B {y | y= BX}

Y= BX

AY=ABX

but AB = 0

AY = 0X

then wat?