# How to calculate rank of a matrix in Geogebra

In this lesson you will learn how to calculate the rank of a square matrix in Geogebra.

**What is the rank of a matrix? ** It is the highest order among the square submatrices in the matrix which have a non-zero determinant.

Type in a square matrix.

For example, a 3x3 square root with three rows and three columns.

**Note**. If you don't know how to make a matrix, read our lesson on how to make a matrix in Geogebra.

Use the **MatrixRank()** function to calculate the rank of the matrix.

Write the name of the starting matrix in the round brackets.

Geogebra calculates and displays the rank of the matrix.

**Explanation**. In this case the rank of the matrix is 2 because the determinant of the 3x3 matrix is zero Δ (m1) = 0. Therefore, the rank cannot be three.

At least one minor 2x2 submatrix has a non-zero determinant. For example, the submatrix in blue has the determinant Δ = -2.

The blue submatrix is of order 2 as it has two rows and two columns. Therefore, the highest order among minors with non-zero determinant is two. Any other submatrixes would have an order equal to or less than the one just found.

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