document.write( "Question 866745: If A is a square matrix of order 3 and |A| = – 2, find the value of |–3A|.\r
\n" ); document.write( "\n" ); document.write( "If A = 2B where A and B are square matrices of order 3 × 3 and |B| =
\n" ); document.write( "5, what is |A|?\r
\n" ); document.write( "\n" ); document.write( "If A is a non-singular matrix of order 3 and |A| = – 3 find |adj A|.\r
\n" ); document.write( "\n" ); document.write( "Given a square matrix A of order 3 × 3 such that |A| = 12 find the value
\n" ); document.write( "of |A adj A|.\r
\n" ); document.write( "\n" ); document.write( "If A is a square matrix of order 3 such that |adj A| = 8 find |A|\r
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Algebra.Com's Answer #522537 by rothauserc(4718)\"\" \"About 
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1) |-3A| = -3^3 |A| = -27 times -2 = 54
\n" ); document.write( "2) A = 2B, |2B| = 2^3 times 5 = 40, then |A| = 40
\n" ); document.write( "3) Since A * (adj A) = |A| * I, and A is 3 x 3, we obtain
\n" ); document.write( "|A * (adj A)| = |A|^3 = (-3)^3 = -27
\n" ); document.write( "-27 = |A * adj A| = |A| |adj A| = -3 |adj A|
\n" ); document.write( "therefore |adj A| = 9
\n" ); document.write( "4) |A * (adj A)| = |A|^3 = 12^3 = 1728
\n" ); document.write( "5) |A * (adj A)| = |A|^3
\n" ); document.write( "|A| |adj A| = |A|^3
\n" ); document.write( "|adj A| = |A|^2
\n" ); document.write( "8 = |A|^2
\n" ); document.write( "2.8284271247461900976 = |A|\r
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