Matrix Calculator

Matrix multiplication requires the columns of the left matrix to equal the rows of the right one. A 2x3 times a 3x4 is defined and yields a 2x4; the reverse, 3x4 times 2x3, is not defined at all. Unlike numbers, matrices do not commute, so even when both orders are legal they usually give different results.

During Gauss-Jordan elimination the tool looks for a usable pivot in each column. If the largest remaining value in that column is below 1e-10 it declares the matrix singular, meaning its determinant is zero and no inverse exists. Geometrically, the matrix collapses space onto a lower dimension, so the transformation cannot be undone.

Copy B's values into matrix A. The determinant, inverse, and transpose buttons are all bound to A. The binary operations (add, subtract, multiply) are the only ones that use both matrices.

They are double-precision floating point, rounded to four decimals for display. Integer inputs give exact integer results for addition, subtraction, multiplication, and transpose. Inverses of matrices with fractional entries carry the usual floating point error, so 1/3 displays as 0.3333.

An empty cell is treated as 0 and the calculation proceeds. Only a cell containing something that cannot be parsed as a number raises an error, and it names the position, such as Cell R2C3 is not a valid number. Watch for accidental blanks, because they change the answer without warning you.