Question

evaluate 3*3matrix
$|111 \\ 11 + a1 \\ 111 + b|$

Answer 1

Open the matrix using the first row to find the determinant
1*[(1+a)(1+b)-1] - 1*[1*(1+b)- 1]  + 1*[1-(1+a)]
= a + b - b + (-a)
= 0