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No, the determinant is a scalar value that can be positive, zero, or negative. It is explicitly not a matrix absolute value, despite the notation $|A|$ sometimes being used.

Conditions: The object is a square matrix.; The notation $|A|$ or $\det(A)$ is being interpreted.

No, the determinant is a scalar value that can be positive, zero, or negative. It is explicitly not a matrix absolute value, despite the notation $|A|$ sometimes being used.

Conditions: The object is a square matrix.; The notation $|A|$ or $\det(A)$ is being interpreted.

For a 2x2 matrix $A=\begin{bmatrix}a&b\\c&d\end{bmatrix}$, the determinant is calculated as $ad-bc$. A square matrix is invertible exactly when its determinant is nonzero.

Conditions: The matrix must be a 2x2 square matrix for the specific formula.; The matrix must be square for the invertibility condition to apply.

For a 2x2 matrix $A=\begin{bmatrix}a&b\\c&d\end{bmatrix}$, the determinant is calculated as $ad-bc$. A square matrix is invertible exactly when its determinant is nonzero.

Conditions: The matrix must be a 2x2 square matrix for the specific formula.; The matrix must be square for the invertibility condition to apply.