If A is an orthogonal matrix, then | MATH - TYPES OF MATRICES, ALGEBRA OF MATRICES | SolveeIt | Solveeit

Today, August 18

Question

If A is an orthogonal matrix, then

A

|A| = 1

B

|A| = 0

C

|A| = ± 1

D

|A| = 2

Answer

|A| = ± 1

Explanation

Solution

AA' = | I | (Q is orthogonal)

|AA'| = | I |, | A | | A' | = 1

| A |² = 1, | A | = ±1