Questions: Consider the following matrix. A= [ [ -4 -6 ] [ 2 3 ] ] Choose the correct description of A. Find A^-1 if it exists. A is nonsingular. That is, it has an inverse. A^-1= A is singular. That is, its inverse doesn't exist.

Solution Steps

To determine if the matrix \( A \) has an inverse, we first calculate its determinant. The matrix is given by:

\[ A = \begin{bmatrix} -4 & -6 \\ 2 & 3 \end{bmatrix} \]

The determinant \( \text{det}(A) \) is calculated as follows:

\[ \text{det}(A) = (-4)(3) - (-6)(2) = -12 + 12 = 0 \]

Since the determinant \( \text{det}(A) = 0 \), the matrix \( A \) is singular. This means that it does not have an inverse.

Final Answer