📈college algebra review

key term - Inverse matrix

Definition

An inverse matrix is a matrix that, when multiplied by its original matrix, yields the identity matrix. It is denoted as $A^{-1}$ for a given matrix $A$.

5 Must Know Facts For Your Next Test

  1. The inverse of a matrix exists only if the determinant of the matrix is non-zero.
  2. For a 2x2 matrix $\begin{bmatrix}a & b \\ c & d\end{bmatrix}$, the inverse is calculated as $\frac{1}{ad-bc}\begin{bmatrix}d & -b \\ -c & a\end{bmatrix}$.
  3. If $A$ and $B$ are invertible matrices, then $(AB)^{-1} = B^{-1}A^{-1}$.
  4. The product of a matrix and its inverse results in the identity matrix, i.e., $AA^{-1} = I$.
  5. Inverting larger matrices often involves row reduction or using software tools like MATLAB or Python.

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