Matrix Multiplication Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
Compute [1001][3−257]\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \begin{bmatrix} 3 & -2 \\ 5 & 7 \end{bmatrix}.

Solution

  1. 1
    The first matrix is the identity II. IA=AIA = A.
  2. 2
    Result: [3−257]\begin{bmatrix} 3 & -2 \\ 5 & 7 \end{bmatrix}.

Answer

[3−257]\begin{bmatrix} 3 & -2 \\ 5 & 7 \end{bmatrix}
The identity matrix II is the multiplicative identity for matrices: IA=AI=AIA = AI = A. It has 1s on the diagonal and 0s elsewhere, analogous to multiplying a number by 1.

About Matrix Multiplication

Multiplying matrices AA (m×nm \times n) and BB (n×pn \times p) by taking dot products of rows of AA with columns of BB to produce an m×pm \times p result.

Learn more about Matrix Multiplication →

More Matrix Multiplication Examples

Example 1 medium

Compute [formula].

Example 2 hard

Compute [formula].

Example 3 easy

Can you multiply a [formula] matrix by a [formula] matrix? Why or why not?

← All Matrix Multiplication Examples Matrix Multiplication Concept