Determinant of 2X2 Matrix

det (A) = A_{1,1} \cdot A_{2,2} - A_{2,1} \cdot A_{1,2}

$det (A) = A_"1,1" * A_"2,2" - A_"2,1" * A_"1,2"$

Matrix A

$"Matrix A"$

The Math

This equation computes the determinant of of a two-by-two matrix. Given a square matrix where

A = $((A_11,A_12),(A_21,A_22))$

det(A) = $A_11 * A_22 - A_12 *A_21$
The multiplication pattern for the determinant, which extends to larger square matrices, is along the diagonals. So, the first term is the product of the matrix elements along the diagonal sloping to the right: $A_11 * A_33$ . The second term is the product of the matrix elements along the diagonal sloping to the left: $A_12 * A_21$ .

The terms formed of the product of the right sloping diagonals are positive and the terms formed of the left sloping diagonals are negative.

When added together, you get: det(A) = $A_11 * A_22$ - $A_12 * A_21$ .