Finding the inverse of a matrix is a common task in algebra, linear equations, and applied math. If you’re using a TI-84 calculator, the process is straightforward once you know the key sequences. This guide walks you through the exact steps to calculate an inverse, with examples, error explanations, and tips for verifying results.
What You Need to Know Before Finding the Inverse
- Square matrix only: The TI-84 can only invert square matrices (2×2, 3×3, etc.).
- Non-zero determinant: If the determinant is 0, the matrix is singular and has no inverse.
- Result format: The calculator may display decimals, but you can convert results into fractions.
👉 If you’re working on larger problems or want quick verification, try the free Inverse Matrix Calculator online.
Step 1: Enter Matrix Mode on TI-84
- Press [2nd], then [MATRIX] to open the matrix menu.
- Scroll right to EDIT.
- Select a matrix name, e.g., [A].
- Enter dimensions (e.g., 2×2, 3×3).
- Fill in the elements row by row.
Press [2nd] [MODE] (QUIT) to return to the home screen.
Step 2: Compute the Inverse of a Matrix
- Open the matrix menu again: [2nd] [MATRIX].
- Select [A] under the NAMES menu.
- Press the x⁻¹ button (inverse key).
- Press [ENTER].
Your TI-84 will display the inverse matrix.
Step 3: Worked Examples
Example 1: 2×2 Matrix
A=[2153]A = \begin{bmatrix} 2 & 1 \\ 5 & 3 \end{bmatrix}
- Enter into [A] as a 2×2.
- Compute
A⁻¹.
Result: A−1=[3−1−52]A^{-1} = \begin{bmatrix} 3 & -1 \\ -5 & 2 \end{bmatrix}
Example 2: 3×3 Matrix with Decimals
B=[1.52003−140.52]B = \begin{bmatrix} 1.5 & 2 & 0 \\ 0 & 3 & -1 \\ 4 & 0.5 & 2 \end{bmatrix}
- Enter as [B] (3×3).
- Compute
B⁻¹. - TI-84 shows decimals; use MATH → Frac to convert to fractions if needed.
Step 4: Troubleshooting Common Errors
- ERR: SINGULAR MAT → The matrix cannot be inverted (determinant = 0).
- Dimension Error → You tried to invert a non-square matrix.
- Wrong values → Double-check entries; one mis-typed number changes everything.
Step 5: Verify the Inverse on TI-84
To check if your result is correct:
- Multiply the original matrix by its inverse.
- On TI-84:
A × A⁻¹. - If correct, the product should be the identity matrix.
For quick online verification, use the Inverse Matrix Calculator and compare outputs.
Quick Reference: TI-84 Key Sequences
| Task | Keystroke |
|---|---|
| Define a matrix | [2nd] [MATRIX] → EDIT |
| Call a matrix | [2nd] [MATRIX] → NAMES |
| Inverse operation | x⁻¹ |
| Convert decimals to fractions | MATH → Frac |
FAQs
Can TI-84 find inverse of a 3×3 matrix?
Yes, as long as it’s square and invertible.
Why does TI-84 say “Singular Matrix”?
It means the determinant = 0, so no inverse exists.
How big of a matrix can TI-84 invert?
Up to 10×10.
How do I change results from decimals to fractions?
Press MATH → 1:Frac after getting your result.
Conclusion
The TI-84 calculator makes finding the inverse of a matrix simple if you know the sequence: define → select → press x⁻¹ → compute. Always remember: only square matrices with non-zero determinant are invertible.