## 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