## What are Matrices?

Matrices are an important branch of mathematics, which also helps students understand other mathematical concepts due to the interrelatedness to other branches. A matrix can be defined as an array of numbers or functions arranged in a rectangular order.

A matrix which possesses rows titled “X” and columns titled as “Y” is called as a matrix of an order of X x Y. The major operations carried out with Matrices are the Addition, Subtraction, and Multiplication. Understanding the types of matrices is essential to understand, the other topics better.

### What are the types of Matrices?

Matrices are commonly classified into:

**Column Matrix:-**A matrix which consists of a singular column can be defined as a column matrix.**Row Matrix:-**If a matrix has only a singular row, then it is termed as a row matrix**Square Matrix:-**When the number of rows is equal to the number of columns, then the matrix is defined as a square matrix.**Diagonal Matrix:-**If the diagonal elements are zero in a square matrix, then it can be defined as a diagonal matrix.**Scalar Matrix:-**When the diagonal elements are equal in a diagonal matrix, then this matrix is assumed to be a Scalar matrix.**Identity Matrix:-**An identity matrix can be defined as a square matrix, whose elements in the diagonal are 1, while the other elements are zero.**Zero Matrix:-**In a matrix, when all the elements are zero, it can simply be defined as a null matrix or a zero matrix.

If two square matrices called A and B exist then we can safely assume that AB = BA = 1, where B is the inverse matrix of A and A is the inverse of B. A square matrix, on the other hand, can be termed as the sum of a skew matrix and a symmetric matrix.

### What is determinant of matrix?

A determinant of a matrix is the addition of the products of the elements within a square matrix. If p, q, r, s are the elements in a matrix.

\(\left | A \right |\) = \(\begin{bmatrix} p & q\\ s & r\end{bmatrix}\)Then, the determinant is (ps-qr)

### What is inverse of matrix?

The inverse function is obtained by simply swapping the position of terms. If we take the same terms of the above matrix then, A= \(\begin{bmatrix} p & q\\ s & r\end{bmatrix}\) has the inverse as \(A^{-1}=1/\left | A \right |\begin{bmatrix} s & -q\\ -r & p \end{bmatrix}\)

### Important Questions

- If the matrix P is both symmetric and skew symmetric, then (A) P is a diagonal matrix (B) P is a zero matrix (C) P is a square matrix (D) None of these
- If unit sale prices of p, q and r are ` 3.50, ` 2.50 and ` 1.00, respectively,

find the total revenue in each market with the help of matrix algebra. - Find the gross profit. If the unit costs of the above three commodities are ` 3.00, ` 2.00 and 100 paise respectively.
- If P and Q are symmetric matrices, prove that PQ-QP is a skew symmetric

Matrix. - Show that the matrix P= \(\begin{bmatrix} 1 &-1 &5 \\ -1 &2 &1 \\ 5 &1 &3 \end{bmatrix}\)

Also Read:

Transpose of a Matrix | Symmetric Matrix and Skew-Symmetric Matrix |

Algebra of Matrices | Matrix Multiplication |