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There are exactly 36 such matrices: 148726593, 157836492, 175429863, 184539762, 249715683, 267935481, 276418953, 294638751, 359814672, 368924571, 386517942, 395627841, 418953276, 429863175, 481267935, 492157836, 517942386, 539762184, 571368924, 593148726, 627841395, 638751294, 672359814, 683249715, 715683249, 726593148, 751294638, 762184539, 814672359, 836492157, 841395627, 863175429, 924571368, 935481267, 942386517, 953276418.
148726593, 157836492, 175429863, 184539762, 249715683, 267935481, 276418953, 294638751, 359814672, 368924571, 386517942, 395627841, 418953276, 429863175, 481267935, 492157836, 517942386, 539762184, 571368924, 593148726, 627841395, 638751294, 672359814, 683249715, 715683249, 726593148, 751294638, 762184539, 814672359, 836492157, 841395627, 863175429, 924571368, 935481267, 942386517, 953276418.
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_Zak Seidov (zakseidov(AT)yahoo.com), _, Jan 18 2011
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Cf. A088215 (1/36)*number of ways to express n as the determinant of a 3 X 3 matrix with elements 1..9.
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Lexicographically ordered 3X3 matrices containing digits numbers 1..9 with maximal determinant = 412.
The matrices are presented here as 9-digit decimal numbers, one digit per entry in the matrix.
148726593, 157836492, 175429863, 184539762, 249715683, 267935481, 276418953, 294638751, 359814672, 368924571, 386517942, 395627841, 418953276, 429863175, 481267935, 492157836, 517942386, 539762184, 571368924, 593148726, 627841395, 638751294, 672359814, 683249715, 715683249, 726593148, 751294638, 762184539, 814672359, 836492157, 841395627, 863175429, 924571368, 935481267, 942386517, 953276418.
368924571,386517942,395627841,418953276,429863175,481267935,492157836,517942386,539762184
571368924,593148726,627841395,638751294,672359814,683249715,715683249,726593148,751294638
762184539,814672359,836492157,841395627,863175429,924571368,935481267,942386517,953276418
nonn,fini,fullbase
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