document.write( "Question 1021823: If A is a non singular matrices of order 3 and |A|=-3 find |adj. A| \n" ); document.write( "

Algebra.Com's Answer #637554 by robertb(5830) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"abs%28adjA%29+=+abs%28A%29%5E%28n-1%29\"$ by a property of the adjoint operator.\r
\n" ); document.write( "\n" ); document.write( "==> $\"abs%28adjA%29+=+abs%28A%29%5E%28n-1%29+=+abs%28A%29%5E2+=+%28-3%29%5E2+=+9\"$ , where n = 3.\r
\n" ); document.write( "\n" ); document.write( "Proof.\r
\n" ); document.write( "\n" ); document.write( "For an invertible nxn matrix, $\"A%2A%28adjA%29+=+abs%28A%29I%5Bn%5D%29\"$ \r
\n" ); document.write( "\n" ); document.write( "==> $\"abs%28A%29abs%28adjA%29+=+%28abs%28A%29%29%5En\"$ ,
\n" ); document.write( "the last equation arising from the determinant of a scalar matrix and the identity matrix.\r
\n" ); document.write( "\n" ); document.write( "==> $\"abs%28adjA%29+=+%28abs%28A%29%29%5E%28n-1%29\"$ , since $\"abs%28A%29+%3C%3E0\"$ \n" ); document.write( "

\n" );