Let A be any 2-by-2 matrix, and let s be any real-valued scalar. Show that det (sA) = s^{2}* det (A).

A = [ a b ] sA = [ sa sb ]

[ c d ] [ sc sd ]

det(A) = ad - cb

det(sA) = (sa)(sd) - (sc)(sb)

= s^2(ad) - s^2(cb)

= s^2 * det(A)

This seems too easy?