Two by Two Matrices - Adding, Subtracting, Multiplying and Inverses
Adding and subtracting matrices is quite simple and is illustrated below.
Suppose we want to find 2A+3B. We multiply every entry in the matrix A by 2 and every entry in the matrix B by 3:
Now we can add entry by entry:
Suppose we want to find 2A-3B. We multiply every entry in the matrix A by 2 and every entry in the matrix B by 3:
Now we can subtract entry by entry:
Suppose we want to find AB, also written as A*B . We multiply the rows of A by the columns of B as shown
Finding the inverse is also quite simple:
Step by Step Guide to Finding the Inverse of a 2 by 2 matrix
Swap the left leaning diagonals a and d.
Change the signs of the right leaning diagonals b and c.
Multiply the diagonal numbers and subtract one product from another. Multiply the matrix by the reciprocal of this number.
Example: Find the inverse of