Inverse Matrix Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Find the inverse of [4131]\begin{bmatrix} 4 & 1 \\ 3 & 1 \end{bmatrix}.

Solution

  1. 1
    det⁡=4−3=1\det = 4 - 3 = 1.
  2. 2
    A−1=[1−1−34]A^{-1} = \begin{bmatrix} 1 & -1 \\ -3 & 4 \end{bmatrix}.

Answer

[1−1−34]\begin{bmatrix} 1 & -1 \\ -3 & 4 \end{bmatrix}
When the determinant is 1, the inverse has integer entries. Swap the diagonal, negate the off-diagonal — no division needed since det⁡=1\det = 1.

About Inverse Matrix

The inverse of a square matrix AA, written A−1A^{-1}, is the unique matrix such that AA−1=A−1A=IAA^{-1} = A^{-1}A = I (the identity matrix). A matrix has an inverse if and only if its determinant is nonzero.

Learn more about Inverse Matrix →

More Inverse Matrix Examples

Example 1 medium

Find the inverse of [formula].

Example 2 easy

Find the inverse of [formula].

Example 4 hard

Does [formula] have an inverse? Explain.

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