Matrix Calculator

Use this matrix calculator for common operations on fixed 2 by 2 matrices. It can add, subtract, and multiply matrices A and B, or find the determinant or transpose of matrix A. It is useful for algebra, linear transformations, graphics, engineering, and homework checks.

How to use this calculator

Choose an Operation, then enter the four entries of matrix A. For addition, subtraction, and multiplication, also enter the four entries of matrix B. The result shows either a result matrix with each entry or the determinant of A.

How it works

For addition and subtraction, matching entries are combined. For multiplication, each output entry is the row of A dotted with the column of B. The 2 by 2 determinant uses:

$det(A) = a11 \times a22 - a12 \times a21$

For example, if A is [1, 2; 3, 4], then det(A) = 1×4 − 2×3 = -2. If B is [5, 6; 7, 8], A plus B gives [6, 8; 10, 12].

Interpreting results

A zero determinant means the 2 by 2 matrix is singular and does not have an inverse, though this form does not calculate inverses. A transpose swaps rows and columns. Related tools include the cross product calculator, statistics calculator, and weighted average calculator.