Determinant of a 2×2 Matrix Calculator

This Determinant of a 2×2 Matrix Calculator helps you find the determinant of a 2×2 matrix and shows each step clearly. It works by multiplying the entries on one diagonal, multiplying the entries on the other diagonal, and then subtracting the second product from the first. This makes it useful for checking answers, understanding how a determinant is calculated, and practising linear algebra step by step.

Step-by-step method

1. Write the 2×2 matrix a = [[a, b], [c, d]].
2. Use the determinant formula det(a) = a·d − b·c.
3. Substitute values and compute the result.

Determinant formula

Example 1: det(a) for a 2×2 matrix

Step 1 - Write the 2×2 matrix a = [[a, b], [c, d]].

In this problem: We start with the given 2×2 matrix.

Step 2 - Use the determinant formula det(a) = a·d − b·c.

In this problem: Use the 2×2 determinant rule.

Step 3 - Substitute values and compute the result.

In this problem: Substitute the entries into the formula.

Step 4 - Simplify to get the final value.

In this problem: Compute the arithmetic.

Final answer: -2

Example 2: det(a) for a 2×2 matrix

Step 1 - Write the 2×2 matrix a = [[a, b], [c, d]].

In this problem: We start with the given 2×2 matrix.

Step 2 - Use the determinant formula det(a) = a·d − b·c.

In this problem: Use the 2×2 determinant rule.

Step 3 - Substitute values and compute the result.

In this problem: Substitute the entries into the formula.

Step 4 - Simplify to get the final value.

In this problem: Compute the arithmetic.

Final answer: -33