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Algebra

Notation of matricesAlgebra

Adding and subtracting matricesAlgebra

Scalar multiplicationAlgebra

Matrix multiplication- Home
- Precalculus
- Properties of Matrices

Still Confused?

Try reviewing these fundamentals first.

Algebra

Notation of matricesAlgebra

Adding and subtracting matricesAlgebra

Scalar multiplicationAlgebra

Matrix multiplicationStill Confused?

Try reviewing these fundamentals first.

Algebra

Notation of matricesAlgebra

Adding and subtracting matricesAlgebra

Scalar multiplicationAlgebra

Matrix multiplicationNope, I got it.

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Get Started Now- Intro Lesson6:19
- Lesson: 1a10:16
- Lesson: 1b5:00
- Lesson: 1c3:36
- Lesson: 1d4:08
- Lesson: 1e4:27
- Lesson: 2a5:02
- Lesson: 2b4:21
- Lesson: 2c3:39
- Lesson: 2d3:56

In this lesson, we will learn about identity matrices. Identity matrix is an n by n matrix which all entries diagonal from the top left to the bottom right are 1's, and the rest of the entries are 0. There are many types of identity matrices, as listed in the notes section. We will learn how to apply matrix operations with these such as adding, subtracting, and multiplying. Lastly, we will see that identities have a special property. If two matrices are multiplicative inverses, then multiplying them would give an identity matrix.

Basic concepts: Notation of matrices, Adding and subtracting matrices, Scalar multiplication, Matrix multiplication,

An **identity** matrix is an $n$ by $n$ matrix (written as
$I_n$) where all the entries that is diagonal from the top
left to the bottom right are all 1’s, and the rest of the entries are 0. For example,

are all**identity** matrices.

are all

- Introductiona)The Identity Matrixb)Multiplicative Inverses
- 1.
**Matrix Operation with the Identity Matrix**

You are given that and . Perform the following matrix operations:a)$I_3 \cdot A$b)$2A+4I_3$c)$-4B+2I_2$d)$I_2 \cdot B$e)$0 \cdot I_4$ - 2.
**Multiplicative Inverses**

Are the following matrices multiplicative inverses of each other?

a)

b)

c)

d)

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