Casio fx-991 Matrix Mode: Determinants and Inverses | CalcNova
Casio fx-991 Matrix Calculator Guide
On a Casio fx-991 you enter matrices in Matrix mode, set the size, fill in the elements, then add, multiply, take determinants, inverses and transposes. Below are the rules and worked examples (for instance det of 1,2],[3,4 is −2) to verify your own entries.
Which models have matrix mode
Casio’s fx-991ES PLUS manual lists a MATRIX calculation mode, alongside CMPLX, STAT, BASE-N, EQN, TABLE and VECTOR. The fx-991EX and fx-991CW also provide matrix calculation, but maximum matrix size and menu layout can differ by model, so check your manual for the size limit before entering a large matrix.
Entering a matrix
- Open the calculation-mode menu and select Matrix. On the ES PLUS this is the MODE key; on the CW it is the HOME screen.
- Choose a matrix slot (for example MatA) and set its dimensions, rows × columns.
- Type each element and press = to move to the next.
- Leave the editor, then recall matrices into an expression from the matrix menu.
Add, multiply, determinant, inverse
| Operation | Rule | How it is entered |
|---|---|---|
| Add / subtract | Same size only; element by element | MatA + MatB |
| Multiply | Columns of the first must equal rows of the second | MatA × MatB |
| Determinant | Square matrices only | det( ) from the matrix menu |
| Inverse | Square, non-zero determinant | MatA followed by the x-1 key |
| Transpose | Swaps rows and columns | Trn( ) from the matrix menu |
The matrix menu is reached with a SHIFT key combination that varies by model; use your manual to find the exact key.
Worked examples to check against
Let A = 1, 2], [3, 4 and B = 5, 6], [7, 8.
- A + B = 6, 8], [10, 12.
- A × B: row 1 = (1×5 + 2×7, 1×6 + 2×8) = (19, 22); row 2 = (3×5 + 4×7, 3×6 + 4×8) = (43, 50). So A × B = 19, 22], [43, 50.
- det A = 1×4 − 2×3 = −2.
- A-1 = (1/det) × 4, −2], [−3, 1 = −2, 1], [1.5, −0.5.
- Transpose of A = 1, 3], [2, 4.
If your calculator returns these values, your entry is correct. Order matters: B × A = 23, 34], [31, 46, which differs from A × B.
Matrix inverse also solves linear systems. For 2x + y = 5 and x + 3y = 10, write A = 2, 1], [1, 3, then [x, y] = A-1 × [5, 10]. det A = 5, so A-1 = (1/5) × 3, −1], [−1, 2, giving x = (15 − 10)/5 = 1 and y = (−5 + 20)/5 = 3. Check: 2(1) + 3 = 5 and 1 + 3(3) = 10. For equations specifically, the EQN mode may be faster; see the advanced functions guide.
Common errors
- Dimension error: adding or multiplying matrices with incompatible sizes.
- Math error on inverse: the determinant is zero, so no inverse exists.
- Wrong slot: editing MatA but recalling MatB. Check which slot holds which data.
- Lost data: a full reset clears matrix memory; see the reset guide.
The CalcNova online calculator has its own matrix mode (up to 4×4: add, subtract, multiply, determinant, inverse, transpose) that is handy for checking answers.
Frequently asked questions
- Can I multiply a 2×3 by a 3×2 matrix?
- Yes. The result is 2×2.
- Why is my inverse an error?
- The matrix is singular (determinant 0) or not square.
- Do all fx-991 models support matrices?
- The ES PLUS, EX and CW all have matrix calculation, but sizes and menus differ. Confirm in your manual.