Works with 2×2 and 3×3 matrices and covers the core operations: addition, subtraction, multiplication, transpose, determinant, and inverse. Enter both matrices A and B and every applicable result calculates at once, so you can compare operations side by side.
The determinant is calculated using cofactor expansion along the first row, and the inverse is the adjugate matrix (the transpose of the cofactor matrix) divided by the determinant — the same method taught in a standard linear algebra course.
When a matrix's determinant is zero, it has no inverse — the calculator shows "Not invertible — determinant is 0" rather than an error, since a zero determinant is a valid, meaningful mathematical result in its own right, not a broken calculation.
2×2 and 3×3 matrices. Addition, subtraction, and multiplication apply where the dimensions are compatible; determinant, transpose, and inverse are calculated for each matrix individually.
By cofactor expansion along the first row — the standard method for 2×2 and 3×3 matrices, matching what you'd compute by hand or see in a textbook.
A matrix only has an inverse when its determinant is non-zero. If the determinant works out to exactly 0, the matrix is singular and has no inverse — this is a correct mathematical result, not an error.
Only when their dimensions are compatible for multiplication (the number of columns in the first must match the number of rows in the second). Incompatible sizes won't produce a multiplication result.
