The Purplemath Forums

by **testing** on Sun Mar 01, 2009 7:15 pm

Let A be any 2-by-2 matrix, and let s be any real-valued scalar. Show that det (sA) = s² * 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?

**Sponsor**

by **stapel_eliz** on Sun Mar 01, 2009 7:35 pm

Sometimes it is that easy! :wink:

by **testing** on Wed Mar 04, 2009 7:35 pm

Thanks.

The Purplemath Forums

For 2-by-2 matrix A, show that det(sA) = s^2 * det(A)

For 2-by-2 matrix A, show that det(sA) = s^2 * det(A)

Re: For 2-by-2 matrix A, show that det(sA) = s^2 * det(A)