Question 1

What can this matrix calculator do?

Accepted Answer

It performs matrix addition and subtraction, matrix multiplication, transpose, determinant, and inverse for 2x2 and 3x3 matrices. You can switch the size and choose the operation from the toolbar.

Question 2

When can two matrices be multiplied?

Accepted Answer

Two matrices A (m x n) and B (p x q) can be multiplied only when the number of columns of A equals the number of rows of B (n = p). For square matrices of the same size this is always satisfied.

Question 3

How is the determinant of a 3x3 matrix calculated?

Accepted Answer

Using cofactor expansion along the first row: det = a11*M11 - a12*M12 + a13*M13, where each M is the 2x2 minor obtained by deleting the corresponding row and column.

Question 4

Does a matrix always have an inverse?

Accepted Answer

No. Only square matrices with a non-zero determinant are invertible. If the determinant is zero the matrix is singular and has no inverse.