Maths - Matrix algebra - 2D arithmatic

The following calculator allows you to calculate 2x2 matrix arithmetic. Enter the values into the matrix into the top two matries and then press "+ - or * " to display the result in the bottom matrix:

=

To add matrices just add the corresponding elements, for 2x2 matrices and then,

 a00 + b00 a01 + b01 a10 + b10 a11 + b11
=
 a00 a01 a10 a11
+
 b00 b01 b10 b11

Matrix Subtraction

To subtract matrices just subtract the corresponding elements, for 2x2 matrices and then,

 a00 - b00 a01 - b01 a10 - b10 a11 - b11
=
 a00 a01 a10 a11
-
 b00 b01 b10 b11

Matrix Multiplication

For 2x2 matrices then,

 a00*b00 + a01*b10 a00*b01 + a01*b11 a10*b00+ a11*b10 a10*b01 + a11*b11
=
 a00 a01 a10 a11
 b00 b01 b10 b11

This is worked out as follows: for each entry in the matrix we take the row from the first operand and the column from the second operand:

 a00 a01 a10 a11
 b00 b01 b10 b11
=
 a00 a01
 b00 b10
 a00 a01
 b01 b11
 a10 a11
 b00 b10
 a10 a11
 b01 b11

This single row times a single column is equivalent to the dot product:

 a00 a01 a10 a11
 b00 b01 b10 b11
=
 a00*b00 + a01*b10 a00*b01 + a01*b11 a10*b00 + a11*b10 a10*b01 + a11*b11