Let A be a 3 3 matrix such that A + A ^ T = O . If A [ array c 1 -1 0 array ]= [ array l 3 3 2 array ], A ² [ array c 1 -1 0 array ]= [ array c -3 19 -24 array ] and det ( adj (2 adj ( ~A + I )))=(2)^ (3)^ (11)^ , , , are non-negative integ

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Let A be a 3 3 matrix such that A + A ^ T = O . If A [ array c 1 -1 0 array ]= [ array l 3 3 2 array ], A ² [ array c 1 -1 0 array ]= [ array c -3 19 -24 array ] and det ( adj (2 adj ( ~A + I )))=(2)^ (3)^ (11)^ , , , are non-negative integers, then + + is equal to _ _ _ _

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A is skew-symmetric: A = bmatrix 0 & -c & b & 0 & -a -b & a & 0 bmatrix . From A bmatrix 1 -1 0 bmatrix = bmatrix 3 3 2 bmatrix : c = 3 , a+b = -2 . From A^2 bmatrix 1 -1 0 bmatrix = bmatrix -3 19 -24 bmatrix : b = 3 , a = -5 . A+I = bmatrix 1&-3&3 3&1&5 -3&-5&1 bmatrix , (A+I) = 44 . For 3 3 matrix: ( adj (M)) = ( M)^2 . (2 , adj (A+I)) = 8 44^2 = 8 1936 = 15488 = 2^7 11^2 . ( adj (2 , adj (A+I))) = 15488^2 = 2¹⁴ 11^4 . = 14, = 0, = 4 . + + = 18 .

Let A be a 3 3 matrix such that A + A ^ T = O . If A [ array c 1 -1 0 array ]= [ array l 3 3 2 array ], A ² [ array c 1 -1 0 array ]= [ array c -3 19 -24 array ] and det ( adj (2 adj ( ~A + I )))=(2)^ (3)^ (11)^ , , , are non-negative integers, then + + is equal to _ _ _ _

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