Square matrix based problem

Question

Question 1: For what value of a and b is dim Nul A = 1, where

You must provide reasoning to justify your answer.

Question 2: Assume the columns, denoted a₁, a₂, . . . an of a square matrix A form an orthonormal basis of Rⁿ. Show that A^T = A^-1.

Note that when writing a proof you should present an argument with a clear logical structure and explain each step carefully.