A matrix A is idempotent if \(\mathbf A^2 = \mathbf A\) What are the possible values of \(\det\mathbf A\)?
If \(\mathbf A^2 = \mathbf A\), then \(\left(\det \mathbf A\right)^2 = \det \mathbf A\),
which means \(\det \mathbf A\) = 0 or 1