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Last updated at Jan. 22, 2020 by Teachoo
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Ex 4.5, 3 Verify A (adj A) = (adj A) A = |๐ด| I, where A = [โ 8(2&3@โ4&โ6)] Let A = [โ 8(2&3@โ4&โ6)] adj A = [โ 8(2&3@โ4&โ6)] = [โ 8(โ6&โ3@4&2)] |๐ด| = |โ 8(2&3@โ4&โ6)| = 2 ร (โ6) โ 3 ร (โ4) = โ12 + 12 = 0 Calculating A (adj A) = [โ 8(2&3@โ4&โ6)] [โ 8(โ6&โ3@4&2)] = [โ 8(2 ร(โ6)+3 ร4&2 รโ3+3ร2@โ4 ร(โ6)+(โ6) ร4&โ4 ร(โ3)+(โ6) ร2)] = [โ 8(โ12+12&โ6+6@+ 24 โ24&12โ12)] = [โ 8(0&0@0&0)] Similarly (adj A)A = [โ 8(โ6&โ3@4&2)] [โ 8(2&3@โ4&โ6)] = [โ 8(โ 6(2)+(โ3) (โ4)&โ6(3)+(โ3)(โ6)@4(2)+2(โ4)&4 (3)+2 (โ6))] = [โ 8(โ12+12&โ18+18@8 โ 8&12โ12)] = [โ 8(0&0@0&0)] Also |A| I = 0I = O โด A (adj A) = (adj A)A = |A|I Hence Proved
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