Note: I'm using (A^T) for the transpose of A.

Problem: Find (A^T)A (the inner product of A with itself) if the columns of A are unit vectors, all mutually perpendicular.

My work: if the columns of A are a(1), a(2),..., a(n) then (A^T)A = ||a(1)||^2 + ||a(2)||^2 + ... + ||a(n)||^2 = 1+1+...+1 = n, so the answer is the number of columns (n) in A. Did I do this correctly?