Math Problem Statement

  1. Sabiendo que A y B son dos matrices de orden 2 tales que |𝐴| = − 2 y |𝐵| = 4, calcula, justificando la respuesta: |𝐴𝐵௧ | ; |𝐴 ௧ | ; |𝐵 ିଵ| ; |𝐴 ିଵ𝐵|; |3𝐴|.

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Matrices
Determinants

Formulas

Determinant of a product: |AB| = |A| * |B|
Determinant of a transpose: |A^T| = |A|
Determinant of an inverse: |A^-1| = 1 / |A|
Determinant of a scalar multiplication: |cA| = c^n * |A| for an n x n matrix

Theorems

Properties of determinants: product, transpose, inverse, scalar multiplication

Suitable Grade Level

Grades 11-12 or University level