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Get access to the detailed solutions to the previous years questions asked in IIM IPMAT exam
Let the sum of all three elements along any row, column or diagonal be S.
Then, f = S – (8 + 3) = S – 11 …...(i) (from the bottom row)
d = S – (7 + f) …....(ii) (from one of the diagonals)
From equations (i) and (ii), we get
d = S – (7 + S – 11)
∴ d = 4
Also, b = S – (8 + d) = S – 12 (from the middle column) …....(iii)
a = S – (b + 7) (from the first row)…....(iv)
From equations (iii) and (iv), we get a = 5 & b = 0
∴ S = 12
∴ The matrix A comes out to be 
Determinant |A| = 5(4 × 3 − 8 × 2) + 0(2 × 1 − 6 × 3) + 7(6 × 8 − 1 × 4)
= 5(12 − 16) + 0 + 7(48 − 4)
= − 20 + 0 + 308 = 288