A matrix is a grid of numbers. It has rows and columns. A 2×3 matrix has two rows and three columns. Matrices organize data and represent linear transformations. They can be added, multiplied, and inverted under certain conditions.

Matrix multiplication is not commutative: AB usually differs from BA. The identity matrix acts like 1, leaving other matrices unchanged when multiplied. The determinant measures how a matrix scales area or volume; if it is zero, the matrix has no inverse.

Matrices appear in computer graphics, where they rotate and scale 3D objects. In statistics, they organize data for regression. In physics, they represent quantum operators. In engineering, they solve systems of equations. The concept is simple to state but rich in theory and application.

• Rectangular array of numbers
• Multiplication is not commutative
• Determinant measures scaling
• Used in graphics, statistics, physics, and engineering