#Matrices: Inverses & Determinants - Your Night-Before Review 🚀

Hey, future AP Pre-Calculus master! Let's make sure you're feeling super confident about matrices. We're going to break down inverses and determinants so they're crystal clear. Ready? Let's go!

#4.11 The Inverse and Determinant of a Matrix

# 🤸 Identity Matrix and Inverses

• Identity Matrix (I): Think of it as the '1' of matrices. When you multiply any matrix by the identity matrix, you get the original matrix back. It's a square matrix with 1s on the main diagonal and 0s everywhere else. 🤯

• Size: It's always n x n (square), where n is the number of rows and columns. ↗️

• Main Diagonal: The diagonal from the top left to the bottom right is where the 1s live. 1️⃣

• Inverse Matrix (A⁻¹): If you multiply a square matrix (A) by its inverse (A⁻¹), you get the identity matrix (I). A * A⁻¹ = A⁻¹ * A = I 😁

• 2x2 Inverse Formula: For a 2x2 matrix A =
  $$\begin{bmatrix} a & b \\ c & d \end{bmatrix}$$, the inverse is: $$A^{-1} = \frac{1}{det(A)} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}$$ where det(A) = ad - bc.

Identity matrices: Note the 1s along the main diagonal and 0s elsewhere.

*Inverse of a 2x2 matrix: Swap the diagonal, negate the off-diagonal, and divide by the deter...