How to Find Inverse of a Matrix in Casio fx-991EX – Complete Guide

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The Casio fx-991EX (ClassWiz) is one of the most popular scientific calculators used by students and professionals. It comes with powerful features for matrix calculations, including the ability to compute the inverse of a matrix quickly. Whether you are solving linear equations, checking homework, or preparing for exams, knowing how to use your fx-991EX for matrix inverses will save you time.

This guide will walk you through step-by-step instructions for finding the inverse of a matrix in the Casio fx-991EX. You’ll also see worked examples, troubleshooting tips, and how to verify your results using the free Inverse Matrix Calculator.

Key Concepts Before You Start

Step-by-Step: How to Invert a Matrix in Casio fx-991EX

1. Enter Matrix Mode

  • Press MODE.
  • Choose 6: Matrix.

2. Define the Matrix

  • Press OPTN → 2 (Matrix).
  • Select 1: Dim to set the dimensions.
  • Pick a slot (MatA, MatB, or MatC).
  • Choose 2×2 or 3×3.
  • Enter the values row by row, pressing = after each element.

3. Access the Matrix

  • Press AC to return to the main screen.
  • Press OPTN → 2 (Matrix).
  • Select MatA (or the slot you used).

4. Apply the Inverse Operation

  • With MatA on screen, press the x⁻¹ button.
  • The display should show MatA⁻¹.

5. Calculate

  • Press =.
  • The inverse matrix will appear.
  • Use S⇔D to switch between fractions and decimals.

Worked Examples

Example 1: 2×2 Matrix

A=[2134]A = \begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix}

Steps: Enter as MatA → Compute MatA⁻¹.
Result: A−1=[0.8−0.2−0.60.4]A^{-1} = \begin{bmatrix} 0.8 & -0.2 \\ -0.6 & 0.4 \end{bmatrix}

or as fractions: [45−15−3525]\begin{bmatrix} \tfrac{4}{5} & -\tfrac{1}{5} \\ -\tfrac{3}{5} & \tfrac{2}{5} \end{bmatrix}

Example 2: 3×3 Matrix with Decimals

B=[1−230.54−1205]B = \begin{bmatrix} 1 & -2 & 3 \\ 0.5 & 4 & -1 \\ 2 & 0 & 5 \end{bmatrix}

Steps: Enter as MatA (3×3) → Compute MatA⁻¹.
Result: Displayed as decimals, but you can toggle to fractions if possible.

Example 3: Singular Matrix (No Inverse)

C=[2412]C = \begin{bmatrix} 2 & 4 \\ 1 & 2 \end{bmatrix}

Steps: Enter as MatA (2×2) → Try MatA⁻¹.
Result: Calculator shows “Math ERROR” because determinant = 0.

Common Mistakes and Troubleshooting

  • Non-square matrices → Only square matrices can be inverted.
  • Wrong dimension setting → Always set correct size (2×2 or 3×3).
  • Input errors → Double-check rows and columns.
  • Fraction vs decimal confusion → Use S⇔D to toggle formats.
  • Singular matrix error → Means determinant = 0; no inverse exists.

How to Verify Your Result

The best way to confirm an inverse is correct is to multiply the original matrix by the inverse: A×A−1=IA \times A^{-1} = I

If the product is the identity matrix, your answer is correct.

👉 For quick verification and larger matrices, use the free Inverse Matrix Calculator

FAQs

Q1. Can Casio fx-991EX invert a 4×4 matrix?
No. It supports up to 3×3 matrices.

Q2. What happens if the determinant is zero?
The calculator displays “Math ERROR”, meaning no inverse exists.

Q3. How do I get fractions instead of decimals?
Press S⇔D to toggle the output.

Q4. Can I verify the inverse on fx-991EX itself?
Yes. Multiply MatA × MatA⁻¹ and check if the result is the identity matrix.

Q5. Why is my result approximate?
The fx-991EX may round decimals. Toggle to fractions for exact values when possible.

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