Practice Inverse Matrix in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The inverse of a square matrix A, written A^{-1}, is the unique matrix such that AA^{-1} = A^{-1}A = I (the identity matrix). A matrix has an inverse if and only if its determinant is nonzero.
If matrix A represents a transformation (like rotating 30 degrees), then A^{-1} undoes that transformation (rotating -30 degrees). Multiplying by the inverse is the matrix equivalent of dividing. Just as 5 \times \frac{1}{5} = 1, we have A \cdot A^{-1} = I.
Example 1
mediumFind the inverse of A = \begin{bmatrix} 2 & 1 \\ 5 & 3 \end{bmatrix}.
Example 2
easyFind the inverse of \begin{bmatrix} 1 & 2 \\ 0 & 3 \end{bmatrix}.
Example 3
easyFind the inverse of \begin{bmatrix} 4 & 1 \\ 3 & 1 \end{bmatrix}.
Example 4
hardDoes \begin{bmatrix} 6 & 3 \\ 4 & 2 \end{bmatrix} have an inverse? Explain.