Question

Given that A = [a_ij] is a square matrix of order 3×3 and |A| = −7, then the value of \(\sum_{i=1}^{3}\)a_i2A_i2, where A_ij denotes the cofactor of element a_ij is :

(a) 7

(b) -7

(c) 0

(d) 49

Answer 1

Option : (b) |A| = −7

\(\sum_{i=1}^{3}\) a_i2A_i2

= a₁₂A₁₂ + a₂₂A₂₂ + a₃₂A₃₂ 

= |A| = -7