[a b
   c d]

To solve for discriminant, do ad - bc

Finding InverseEdit

  [a b
   c d]

Switch the locations of a and d, and switch the signs of b and c. Your new matrix should be

  [d -b
   -c a]

Important!!: Don't forget the discriminant in front. That new matrix will be multipled by (1/[discriminant). Simply multiply each value by the fraction, and you will have an inverse matrix.

Solving for x & yEdit

[3 0   [x   =   [6
-3 1]   y]      -7]
  • Find the inverse of matrix A using the previous explanation.
  • Use this formula: A^-1 x C = B
  • Multiply the inverse matrix with C to get a set of 2 values, which will be x on the top and y on the bottom.

Decoding a matrixEdit

  • You will need a 2x2 encoding matrix, which is given if you are decoding. You will have to make your own if you are encoding.
  • Again, if decoding, you will be given a set of values. Enter them into a matrix with only 2 rows (otherwise it is impossible to multiply)
  • Use A^-1 x C to get a new matrix. Each value will correspond to a letter in the alphabet, and you can use that to decode.
Community content is available under CC-BY-SA unless otherwise noted.