For any non-singular matrix A, A^-1 =Question 15Answera.None of theseb.Adj A/ |A|c.1/ Adj A/ |A|d.|A| adj A

To determine the correct expression for the inverse of a non-singular matrix $A$, we reference the relationship between a matrix and its inverse. For any non-singular square matrix $A$:

Relevant Concepts

The inverse $A^{-1}$ of matrix $A$ can be expressed using the following relationship: $A^{-1} = \frac{1}{|A|} \text{Adj}(A)$ Where:

• $|A|$ is the determinant of the matrix $A$.
• $\text{Adj}(A)$ is the adjugate (or adjoint) of matrix $A$.

Analysis and Detail

1. Determinant $|A|$: For the inverse to exist, the determinant must be non-zero.
2. Adjugate $\text{Adj}(A)$: This matrix consists of the cofactors of $A$ transposed. It plays a crucial role in the calculation of the inverse.

Verify and Summarize

Given the expression for the inverse $A^{-1}$, we can compare it to the provided options:

• a. None of these
• b. $\frac{\text{Adj} A}{|A|}$
• c. $\frac{1}{\text{Adj} A/ |A|}$
• d. $|A| \text{Adj } A$

The correct answer, which follows the formula, is:

Final Answer

b. $\frac{\text{Adj} A}{|A|}$