If a matrix A = [[1, 2], [3, 4]], what is the determinant of A?

To find the determinant of the 2x2 matrix A, which is given as:

[

A = \begin{bmatrix}

1 & 2 \

3 & 4

\end{bmatrix},

]

the formula for the determinant of a 2x2 matrix is calculated using the following expression:

[

\text{det}(A) = ad - bc,

]

where the matrix elements are:

[

A = \begin{bmatrix}

a & b \

c & d

\end{bmatrix}.

]

In this case, (a = 1), (b = 2), (c = 3), and (d = 4). Plugging these values into the determinant formula gives:

[

\text{det}(A) = (1)(4) - (2)(3) = 4 - 6 = -2.

]

Thus, the determinant of the matrix A is -2, which aligns with the answer provided. Understanding this formula is crucial as it applies to all 2x2 matrices, allowing for easy computation of their determinants. The result also indicates important properties of the matrix, such as whether it is invert