Adjoint Matrix Calculator
This calculator finds the adjoint (also called the adjugate) of a square matrix, a step used in the standard formula for a matrix inverse and in Cramer's rule. Choose whether you are working with a 2x2 or 3x3 matrix, then enter your values into the matrix grid, which comes pre-filled with example numbers so you can see how it works straight away. As soon as you change a figure, the calculator works out every cofactor by deleting the relevant row and column and applying the checkerboard sign pattern, builds the cofactor matrix, then transposes it to give you adj(A). The results panel shows your original matrix, the cofactor matrix, and the final adjoint side by side, along with the determinant det(A). It then checks its own working by confirming that A multiplied by adj(A) equals det(A) multiplied by the identity matrix, showing a verified pass or a note if the matrix is singular, meaning det(A) equals zero, in which case the adjoint still exists but no inverse does. For 2x2 matrices it also shows the shortcut of swapping the diagonal terms and negating the off-diagonal terms. Use this tool to check homework, to see the cofactor working behind the adjoint method, or as a step before finding the actual inverse with the related Matrix Inverse Calculator. It works with any real-valued 2x2 or 3x3 matrix, including negative and decimal entries.
