If two rows and columns are identical then determinant isQuestion 8Answera.1b.0c.Identity matrixd.-1

1. Break Down the Problem

The problem involves determining the value of the determinant of a matrix with identical rows or columns.

2. Relevant Concepts

In linear algebra, one of the properties of determinants is that if a matrix has two identical rows or two identical columns, the determinant of that matrix is zero. This can be summarized as:

• If $R_i = R_j$ (where $R$ represents rows) or $C_i = C_j$ (where $C$ represents columns), then $\text{det}(A) = 0$ for the matrix $A$.

3. Analysis and Detail

Given the options:

• a. 1: This is not correct, as the determinant cannot be one if there are identical rows or columns.
• b. 0: This option matches our concept that the determinant is zero with identical rows or columns.
• c. Identity matrix: This option does not apply, as the identity matrix has a determinant of 1, and it's not related to having identical rows/columns.
• d. -1: Similar to option a, the determinant cannot be -1 if the conditions are met.

4. Verify and Summarize

Since having identical rows or columns results in a determinant of zero, we verify that option b is indeed correct.

Final Answer

The determinant is 0 (Option b).