How to Find the Determinant of a 2x2 Matrix

Step-by-Step Guide

1. 1

   Step 1: Consider the matrix below.

   A=(abcd){\displaystyle A=\left({\begin{matrix}a&b\\c&d\end{matrix}}\right)}
2. 2

   Step 2: Multiply the upper-left entry by the lower-right entry.

   ad{\displaystyle ad} , bc{\displaystyle bc} , detA=ad−bc{\displaystyle \det A=ad-bc} The formula above is the determinant of a general 2x2 matrix.
   
   It is highly useful to memorize. , B=(98−76){\displaystyle B=\left({\begin{matrix}9&8\\-7&6\end{matrix}}\right)} , (9)(6)=54{\displaystyle (9)(6)=54} , (−7)(8)=−56{\displaystyle (-7)(8)=-56} , detB=54−(−56)=110{\displaystyle \det B=54-(-56)=110}
3. 3

   Step 3: Multiply the upper-right entry by the lower-left entry.

4. 4

   Step 4: Subtract the number you just got from the first product.

5. 5

   Step 5: Consider the matrix below.

6. 6

   Step 6: Multiply the upper-left entry by the lower-right entry.

7. 7

   Step 7: Multiply the lower-left entry by the upper-right entry.

8. 8

   Step 8: Subtract the number you just got from the first product.

Detailed Guide

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