Determine whether A and B are inverses by calculating AB and...

Determine whether A and B are inverses by calculating AB and BA. Do not use a calculator.
$$A=\left[\begin{array}{rr}
-1 & 2 \\
3 & -5
\end{array}\right] ; B=\left[\begin{array}{rr}
-5 & -2 \\
-3 & -1
\end{array}\right]$$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Determinant

The determinant is a scalar obtained from a square matrix that provides important information about the matrix, such as whether it is invertible (a non-zero determinant indicates invertibility). In the case of a 2x2 matrix, the determinant is computed as (ad - bc), which is a quick test for the existence of an inverse.

Inverse Matrix

An inverse matrix for a given square matrix A, denoted A?¹, is a matrix that, when multiplied by A from either side, yields the identity matrix. The existence and properties of inverses are crucial in solving systems of linear equations and in many areas of applied mathematics.

Matrix Multiplication

Matrix multiplication is the process of computing a new matrix where each element is the sum of products of corresponding components from rows of the first matrix and columns of the second matrix. This operation is fundamental in linear algebra for combining linear transformations and is used to verify relationships between matrices.

Identity Matrix

The identity matrix is a special square matrix with ones on the main diagonal and zeros elsewhere. It acts as the multiplicative identity in matrix operations, meaning that multiplying any compatible matrix by the identity matrix leaves the original matrix unchanged. This concept is essential in defining matrix inverses.

Transcript

Please give Ace some feedback