How to Multiply Two Determinants of 2x2 Order

Determinants of 2x2 matrices can be multiplied using a specific formula. Here's a step-by-step guide on how to do it:

Step 1: Write down the two 2x2 matrices
Write down the two matrices in the form:
\[ A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \]
\[ B = \begin{pmatrix} e & f \\ g & h \end{pmatrix} \]

Step 2: Calculate the determinants of each matrix
Calculate the determinants of matrices A and B using the formula:
\[ \text{det}(A) = ad - bc \]
\[ \text{det}(B) = eh - fg \]

Step 3: Multiply the determinants
Multiply the determinants of matrices A and B together to get the determinant of the product matrix:
\[ \text{det}(AB) = \text{det}(A) \times \text{det}(B) \]

Step 4: Write down the product matrix
Write down the product matrix by multiplying corresponding elements from matrices A and B:
\[ AB = \begin{pmatrix} ae+bg & af+bh \\ ce+dg & cf+dh \end{pmatrix} \]

By following these steps, you can successfully multiply two determinants of 2x2 order.