Question

If C_ij denotes the cofactor of element P_ij of the matrix P = `[(1, -1, 2),(0, 2, -3),(3, 2, 4)]`, then the value of C₃₁.C₂₃ is ______.

Options

• 5

• 24

• –24

• –5

Answer 1

If C_ij denotes the cofactor of element P_ij of the matrix P = `[(1, -1, 2),(0, 2, -3),(3, 2, 4)]`, then the value of C₃₁.C₂₃ is 5.

Explanation:

Here, C₃₁ = `(-1)^(3 + 1)|(-1, 2),(2, -3)|`

= 3 – 4

= –1

And C₂₃ = `(-1)^(2 + 3)|(1, -1),(3, 2)|`

= –(2 + 3)

= –5

Thus, C₃₁.C₂₃ = (–1)(–5) = 5