Most Important Selected Qs for JEE AdvancedMathematicsMatrices
A square matrix A with elements from the set of real numbers is said to be orthogonal if A^ =A⁻¹ . If A is an orthogonal matrix, then
Options
- AA^ is orthogonal
- BA ⁻¹ is orthogonal
- CAdj. A=A^
- D|A⁻¹ |=1
Correct answer
B. A ⁻¹ is orthogonal
Step-by-step solution
X A⁻¹ A=I A^ A=I (A^ )^ A^ =I A^ is orthogonal Also, (A⁻¹ )^ = (A^ )⁻¹= (A⁻¹ )⁻¹=A=A A⁻¹ (A⁻¹ )^ =1 A ⁻¹ is orthogonal Next, A A^ =1 |A A^ |=1 |A| |A^ |=1 |A|^2=1 |A|= 1 As Adj. A=|A| A⁻¹=|A| A^ , we cannot say, Adj. A=A^ Also, if |A|=1 , then |A⁻¹ | -1