### What are Matrices?

The matrices that you will see on the ACT math exam will normally be in a two-by-two format.

This means that these types of matrices are represented in a box-like format, consisting of 4 numbers.

Two numbers will be at the top of the matrix, and two numbers will be directly below these on the bottom of the matrix.

#### Performing Operations on Matrices

You will need to know how to add and subtract matrices for the exam.

Learn how to perform operations on matrices by looking at question 1 below.

**Question 1:**

Consider the following matrices:

What is A + B?

A.

B.

C.

D.

E.

**The correct answer is C.**

Add the numbers from each matrix to the numbers of the other matrix that are located in the same positions:

Upper left: −1 + −3 = −4

Upper right: 4 + 2 = 6

Lower left: −7 + 3 = −4

Lower right: 8 + −2 = 6

These numbers form the new matrix as follows:

#### How to Find the Determinant of a Matrix

You might also need to find the determinant of a two-by-two matrix on the exam.

In order to find the determinant, you simply need to multiply the upper left by the lower right and then subtract from this amount from the product of the lower left and upper right.

**Question 2:**

What is the determinant of the following matrix?

A. −20

B. −40

C. 20

D. 40

E. 0

**The correct answer is E.**

Multiply the upper left by the lower right:

2 × −10 = −20

Then multiply the lower left and upper right:

10 × −2 = −20

Then subtract to solve:

−20 − −20 =

−20 + 20 =

0