If `B = [{:(5, 2alpha, 1),(0, 2, 1),(alpha, 3, -1):}]` is the inverse of a `3 xx 3` matrix A, then the sum of all values of `alpha` for which det (A) + 1 =0, is

Options

A. 0
B. `-1`
C. 1
D. 2

Explanation

To solve the problem step by step, we need to find the values of \( \alpha \) such that the determinant of matrix \( A \) plus 1 equals zero, given that matrix \( B \) is the inverse of \( A \).

### Step 1: Understand the relationship between matrices \( A \) and \( B \)

Given that \( B \) is the inverse of \( A \), we have:
\[ \text{det}(B) = \frac{1}{\text{det}(A)} \]
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