Matrix Operations and Inverses

To simplify the matrix multiplication process

To perform row operations to find the inverse

To transform the matrix into a diagonal matrix

To convert the matrix into a 2x2 matrix

Multiplying row 2 by 3 and adding to row 3

Adding row 1 to row 2

Subtracting row 3 from row 1

Dividing row 1 by 2

By dividing row 2 by 2

By adding row 1 to row 2

By subtracting row 3 from row 2

By multiplying row 2 by -4 and adding row 1

Adding row 3 to row 1

Subtracting row 2 from row 1

Dividing row 3 by 3

Multiplying row 1 by 2

Dividing row 2 by 3

Multiplying row 3 by 2

Subtracting row 1 from row 3

Adding row 2 to row 3

7

6

5

4

Multiply row 1 by -1/2

Add row 2 to row 1

Subtract row 3 from row 1

Divide row 1 by 3

A zero matrix

A diagonal matrix

The inverse of matrix A

The original matrix

Their product is an identity matrix

Their product is a scalar matrix

Their product is a zero matrix

Their product is a diagonal matrix

A 4x4 matrix

A 3x3 identity matrix

A 2x2 matrix

A 3x3 matrix with specific values