Matrix solver with step-by-step working
Add, subtract, multiply, transpose, invert or find the determinant of 2×2 and 3×3 matrices, with every entry-by-entry calculation shown rather than the result on its own.
Part of SolveStep's free math solver, alongside dedicated tools for algebra, geometry, statistics, and calculus.
Matrix algebra, entry by entry
Matrix operations are mechanical once you see the pattern: add or subtract lines up corresponding entries, multiplication combines a row of A with a column of B, and the determinant and inverse follow fixed formulas for 2×2 and cofactor expansion for 3×3.
This tool shows that mechanical process directly. Every entry of the result traces back to the specific numbers and operations that produced it, and a zero determinant is flagged clearly instead of failing in silence.
Add & subtract
Result[i][j] = A[i][j] ± B[i][j]
Only works when both matrices are the same size. The tool checks first and explains the mismatch when they are not.
Multiply
R[i][j] = row i of A · column j of B
A's column count must match B's row count; each result entry is shown as a dot product.
Determinant & inverse
det(A) = ad − bc
2×2 by the direct formula, 3×3 by cofactor expansion, with a clear "no inverse" result when det(A) = 0.
Matrix solver FAQ
What matrix operations are supported?
Addition, subtraction, multiplication, transpose, determinant, and inverse, for 2×2 and 3×3 matrices.
What happens if a matrix has no inverse?
If the determinant is 0, the tool tells you directly that the matrix is singular and has no inverse, rather than dividing by zero.
Can I multiply matrices of different sizes?
Yes, as long as the number of columns in A matches the number of rows in B. The tool checks this and explains the mismatch when it fails.
Does it support matrices larger than 3×3?
Not yet. This tool supports 2×2 and 3×3 matrices, which cover the vast majority of introductory linear algebra problems.
Is this a matrix math solver I can use for free?
Yes, completely free and with no sign-up. Enter your matrices and every operation runs in your browser, with the working shown at each step.