Matrix Calculator - Odia Numerals

Why is my matrix inverse showing an error?

A matrix has no inverse when its determinant is zero — this is called a singular matrix. This happens when one row (or column) is a linear combination of other rows, meaning the matrix does not have full rank. The calculator will display an error in this case because the inverse does not exist. Check your matrix for duplicate or proportional rows, which are the most common cause.

What does it mean if the determinant is zero?

A zero determinant means the matrix is singular — it has no inverse and the system of equations it represents has either no solution or infinitely many solutions. In practical terms, if you are solving Ax = b and det(A) = 0, the system is either inconsistent (no solution) or dependent (infinitely many solutions). A non-zero determinant means the system has exactly one unique solution.

How do I multiply two matrices?

Enter your first matrix (e.g., 2×3 matrix), then enter your second matrix. For multiplication to work, the number of columns in the first matrix must equal the number of rows in the second matrix. Select "Multiply" and the calculator will compute the result matrix.

Can I find the inverse of a matrix?

Yes! Enter a square matrix (same number of rows and columns) and select "Inverse". The calculator will compute the inverse if it exists. If the determinant is zero, the matrix is singular and has no inverse — the calculator will notify you.

How do I transpose a matrix?

Transposing flips a matrix over its diagonal, converting rows to columns and vice versa. Enter your matrix and select "Transpose". For example, a 2×3 matrix becomes a 3×2 matrix where the element at position (i,j) moves to position (j,i).

What size matrices can I work with?

The calculator supports matrices of various sizes, typically up to 10×10. You can create rectangular matrices (different row and column counts) for operations like addition and multiplication, or square matrices for operations like determinant and inverse.

Can I add matrices of different sizes?

No, matrix addition and subtraction require matrices of the same dimensions (same number of rows and columns). If you try to add mismatched matrices, the calculator will display an error. Make sure both matrices have identical dimensions before adding or subtracting.

Why are Odia numerals rounder than other Indian numeral scripts?

The rounded shapes come from the historical practice of writing on palm leaves (tala pata) with an iron stylus. Straight horizontal or vertical strokes would tear the leaf fibres, so scribes developed a script with predominantly curved strokes. This practical constraint shaped the script over centuries, and the numerals inherited this rounded character. The same palm-leaf origin explains the similar roundness in Burmese and some Southeast Asian scripts.

Input: A = [[2,1],[5,3]], B = [[1,2],[3,4]]

Result: A × B = [[2×1+1×3, 2×2+1×4],[5×1+3×3, 5×2+3×4]] = [[5,8],[14,22]]