AP®︎ Precalculus: Topic 4.11 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 4.11 of AP Precalculus – The Inverse and Determinant of a Matrix.

Questions List

Topic 4.11

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Question 1 Easy

Which matrix II satisfies AI=AAI=A for every 2×22\times 2 matrix AA?

A[0110]\begin{bmatrix}0&1\\1&0\end{bmatrix}
B[0000]\begin{bmatrix}0&0\\0&0\end{bmatrix}
C[1001]\begin{bmatrix}1&0\\0&1\end{bmatrix}
D[1111]\begin{bmatrix}1&1\\1&1\end{bmatrix}

What You’re Being Tested On:

Explore the learning objectives taken directly from the College Board’s AP® Precalculus Curriculum. Ensure you’re prepared for the exact topics covered on the AP® exam, in-class tests, and quizzes, and gain confidence in your mastery of the material.

Topic 4.11: The Inverse and Determinant of a Matrix

Learning Objective: 4.11.A

Determine the inverse of a \(2 \times 2\) matrix.

Essential Knowledge: 4.11.A.1

The identity matrix, II, is a square matrix consisting of 1s on the diagonal from the top left to bottom right and 0s everywhere else.

Essential Knowledge: 4.11.A.2

Multiplying a square matrix by its corresponding identity matrix results in the original square matrix.

Essential Knowledge: 4.11.A.3

The product of a square matrix and its inverse, when it exists, is the identity matrix of the same size.

Essential Knowledge: 4.11.A.4

The inverse of a 2×22 \times 2 matrix, when it exists, can be calculated with or without technology.

Learning Objective: 4.11.B

Apply the value of the determinant to invertibility and vectors.

Essential Knowledge: 4.11.B.1

The determinant of the matrix A=[abcd]A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} is ad−bcad - bc. The determinant can be calculated with or without technology and is denoted det⁡(A)\det(A).

Essential Knowledge: 4.11.B.2

If a 2×22 \times 2 matrix consists of two column or row vectors from R2\mathbb{R}^2, then the nonzero absolute value of the determinant of the matrix is the area of the parallelogram spanned by the vectors represented in the columns or rows of the matrix. If the determinant equals 0, then the vectors are parallel.

Essential Knowledge: 4.11.B.3

The square matrix AA has an inverse if and only if det⁡(A)≠0\det(A) \ne 0.

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