Table of Contents

## What is property of matrix?

Properties of a Square Matrix In a square matrix, the number of rows and columns are equal. A square matrix is a diagonal matrix in which non-diagonal elements are zeroes. A square matrix is a scalar matrix in which the non-diagonal elements are zeroes, and diagonal elements are the same.

## How many properties of matrix are there?

Let us check the three important properties of matrices. Associative Property: For any three matrices A, B, C following the matrix multiplication conditions, we have (AB)C = A(BC). Here both sides of the matrix multiplication are defined.

**What are the properties of matrix multiplication?**

Properties of Matrix Multiplication

- A(BC) = (AB)C associative.
- A(B + C) = AB + AC distributive.
- (A + B)C = AC + BC distributive.
- There are unique matrices Im and In with. Im A = A In = A multiplicative identity.

### What are the types of properties of matrix?

Properties of Matrix Scalar Multiplication

- Associative Property of Multiplication i.e, (cd)A = c(dA)
- Distributive Property i.e, c[A + B] = c[A] + c[B]
- Multiplicative Identity Property i.e, 1. A = A.
- Multiplicative Property of Zero i.e, 0. A = 0 c.
- Closure Property of Multiplication cA is Matrix of the same dimension as A.

### What is commutative property in matrix?

Commutative Law of Addition of Matrix: Matrix multiplication is commutative. This says that, if A and B are matrices of the same order such that A + B is defined then A + B = B + A.

**What do you mean by determinant?**

Definition of determinant 1 : an element that identifies or determines the nature of something or that fixes or conditions an outcome education level as a determinant of income.

#### How do you use properties of determinants?

If two rows (or columns) of a determinant are identical the value of the determinant is zero. Let A and B be two matrix, then det(AB) = det(A)*det(B). Determinant of diagonal matrix, triangular matrix (upper triangular or lower triangular matrix) is product of element of the principle diagonal.

#### What is Closure property in matrix?

Closure property simply states that if you have a scalar quantity X and a matrix A of the same order m*n, then each element will be multiplied by X. This property states that if any matrix A of order m*n is multiplied by any scalar, then the order of Matrix remains same as m*n.

**What is associative property of multiplication?**

The associative property is a math rule that says that the way in which factors are grouped in a multiplication problem does not change the product.

## What is minor and cofactor?

The minor of an element is equal to the determinant of the matrix remaining after excluding the row and column containing the element. The cofactor of an element is equal to the product of the minor of the element, and -1 to the power of the row and column of the element.

## What is the difference between matrix and determinant?

In a matrix, the set of numbers are covered by two brackets whereas, in a determinant, the set of numbers are covered by two bars. The number of rows need not be equal to the number of columns in a matrix whereas, in a determinant, the number of rows should be equal to the number of columns.