Mathematics | Matrices - Part 6 | Class 12th | Cluster Adda | Vivek Sir

Mathematics | Matrices - Part 6 | Class 12th | Cluster Adda | Vivek Sir

Mathematics | Matrices - Part 5 | Class 12th | Cluster Adda | Vivek Sir - https://youtu.be/LBlTiUNNCmU
Mathematics | Matrices - Part 4 | Class 12th | Cluster Adda | Vivek Sir - https://youtu.be/unzM28uGA78
Mathematics | Matrices - Part 3 | Class 12th | Cluster Adda | Vivek Sir - https://youtu.be/cnhXwUF_6t4
Mathematics | Matrices - Part 2 | Class 12th | Cluster Adda | Vivek Sir -
https://youtu.be/zqBnbt5vW-c
Mathematics | Matrices - Part 1 | Class 12th | Cluster Adda | Vivek Sir -
https://youtu.be/KTXbb-ADVgk

Matrices have several important properties that are useful in various mathematical operations and applications. Here’s a summary of the main properties of matrices:
1. Addition
Matrices can be added if they have the same dimensions (same number of rows and columns).

Addition is commutative

Addition is associative

There exists an additive identity matrix (a zero matrix)

2. Scalar Multiplication
A matrix can be multiplied by a scalar (a real number).

Scalar multiplication is distributive

Scalar multiplication is associative

The identity scalar is 1

3. Multiplication
Matrix multiplication is defined only when the number of columns in the first matrix equals the number of rows in the second matrix.

Matrix multiplication is not commutative:

Matrix multiplication is associative

Matrix multiplication is distributive

There exists a multiplicative identity matrix I (square matrix)

4. Transpose
The transpose of a matrix A is obtained by flipping the matrix over its diagonal.

Transpose of a sum

Transpose of a product

Double transpose

5. Inverse
A matrix A has an inverse if and only if it is square (same number of rows and columns) and its determinant is non-zero.

Not all matrices have an inverse (non-invertible matrices are called singular matrices).

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