Determinant of 2 by 2 solved

Written By: Rachel
Updated On: July 4, 2022
Topic: Blog

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Calculation on determinant of 2 by 2 matrix

Solving any Mathematical problem involving 2 by 2 matrix is simple, so today, we will share with you how to find a determinant of a 2 by 2 matrix correctly.

As you know, 2 by 2 matrix (also written as 2-by-matrix,) is composed of two rows and two columns only.

Determinant is denoted by Det. or |A|.

On the other hand, to find a determinant of 2×2 matrix. You should calculate the product of diagonal from top left and then finding its difference with the product of the diagonal from the top right.

For example;

Supposed matrix;

$https://latex.codecogs.com/svg.image?A = \begin{bmatrix}e & f \\g & h \\\end{bmatrix}$

Find the determinant of the matrix?

$Det.A = (eh - fg)$

{Read as Determinant on matrix A is given by eh (product of first diagonal from left) minus fg (product of second diagonal from right.}

2×2 matrix example calculation

Question

Find the determinant of matrix A given by;

$https://latex.codecogs.com/svg.image?A = \begin{bmatrix}1 & 0 \\ -2& 4\\\end{bmatrix}$

Solution

$https://latex.codecogs.com/svg.image?Det. A = \left\{ (1 \times 4)- (-2 \times 0)\right\}$

$https://latex.codecogs.com/svg.image?Det. A = \left\{ 4 -0 \right\}$

$https://latex.codecogs.com/svg.image?Det. A = \left\{ 4 \right\}$

That is how to calculate determinant of any 2×2 matrix.

Determinant of 2 by 2 solved

2×2 matrix example calculation

Question

Solution

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