# ACT Strategy for Solving a Matrix Using a Determinant

A *determinant* is a common operation performed on a square matrix. On the ACT Math test, the only determinant formula you need to be familiar with is for a 2 x 2 matrix. Here’s the formula for the determinant of

Note that the determinant of a matrix is simply a number, not a matrix. To solve a problem with a determinant, you simply plug the numbers from the matrix into the formula and solve.

### Example 1

What is the determinant of the matrix

(A) –22

(B) –2

(C) 0

(D) 2

(E) 22

First, apply the determinant formula:

Now evaluate to solve the problem:

= 28 – 30 = –2

Therefore, the correct answer is Choice (B).

### Example 2

What is the value of *k* if the determinant of the matrix

equals 16?

(F) –2

(G) –1

(H) 0

(J) 1

(K) 2

Start by applying the determinant formula and then evaluate:

This value equals 16, so create your equation and solve:

So the correct answer is Choice (F).