Matrix Calculator: Multiply, Inverse, Determinant & Power

Enter details

Log in or create a free account to save your inputs and results, so you don't have to enter them again next time.🔒 No spam, ever. We never sell or share your details, and you can delete your history or account at any time. Privacy policy

Fill in the details and click Calculate to see your results.

Formula at a glance

Matrix Calculator: Matrix product — (AB)ᵢⱼ = Σₖ aᵢₖ·bₖⱼ. Example: A × B → A × B: [19, 22; 43, 50] — How the Matrix Calculator works: Matrix product — (AB)ᵢⱼ = Σₖ aᵢₖ·bₖⱼ

Rate this calculator

Was it useful? A quick star rating helps others — and you can leave a comment too.

Rate it: ★ ★ ★ ★ ★

📘 About the Matrix Calculator

Matrices are rectangular arrays of numbers used to solve systems of equations, transform shapes in computer graphics, represent networks, and in statistics, economics and machine learning. Multiplying matrices combines transformations; the inverse undoes one.

Type matrices row by row (1 2; 3 4). The calculator adds, subtracts and multiplies (showing how each entry of A × B is formed), multiplies by a number, transposes, inverts and raises to whole-number powers, and always reports the determinant, rank and trace of A.

🧮 Formula

Matrix product

(AB)ᵢⱼ = Σₖ aᵢₖ·bₖⱼ

Size rule

(m × n)(n × p) = m × p

2 × 2 inverse

A⁻¹ = (1/(ad − bc))·[d −b; −c a]

✏️ Worked examples

A × B

You enter
Matrix A	1 2; 3 4
Operation	A × B
Matrix B	5 6; 7 8
k (scalar or power)	2

You get
A × B	[19, 22; 43, 50]
det(A)	−2
trace(A)	5
rank(A)	2
Size of A	2 × 2

[19, 22; 43, 50].

Power of a shear matrix

You enter
Matrix A	1 1; 0 1
Operation	Power Aᵏ
k (scalar or power)	5

You get
A⁵	[1, 5; 0, 1]
det(A)	1
trace(A)	2
rank(A)	2
Size of A	2 × 2

[1, 5; 0, 1].

🧭 How to use this calculator

What you enter

Matrix ARows separated by ; or new lines, entries by spaces or commas. Fractions like 1/2 are fine.
Operation
Matrix B
k (scalar or power)

What you get

A × B
det(A)
trace(A)
rank(A)
Size of A

❓ Frequently asked questions

Can any two matrices be multiplied?

Only if A has as many columns as B has rows. A 2 × 3 matrix times a 3 × 4 matrix gives a 2 × 4 matrix.

Is matrix multiplication commutative?

No — in general A × B ≠ B × A, and one may exist without the other.

What is the transpose?

The matrix with rows and columns swapped: the first row becomes the first column.

▦ Matrix Calculator: Multiply, Add, Inverse, Power