Inverse Matrix Math Example 2

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

Example 2

easy
Find the inverse of [1203]\begin{bmatrix} 1 & 2 \\ 0 & 3 \end{bmatrix}.

Solution

  1. 1
    Step 1: det⁡=1(3)−2(0)=3\det = 1(3) - 2(0) = 3.
  2. 2
    Step 2: A−1=13[3−201]=[1−23013]A^{-1} = \frac{1}{3}\begin{bmatrix} 3 & -2 \\ 0 & 1 \end{bmatrix} = \begin{bmatrix} 1 & -\frac{2}{3} \\ 0 & \frac{1}{3} \end{bmatrix}.
  3. 3
    Check: [1203][1−2/301/3]=[1001]\begin{bmatrix} 1 & 2 \\ 0 & 3 \end{bmatrix}\begin{bmatrix} 1 & -2/3 \\ 0 & 1/3 \end{bmatrix} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} ✓

Answer

[1−23013]\begin{bmatrix} 1 & -\frac{2}{3} \\ 0 & \frac{1}{3} \end{bmatrix}
Upper triangular matrices have straightforward inverses. The formula still applies: swap diagonal, negate off-diagonal, divide by determinant.

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 3 easy

Find the inverse of [formula].

Example 4 hard

Does [formula] have an inverse? Explain.

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