Question

(is)⁻¹(i−s)(is)(i−s)⁻¹ Commutative skew-symmetric:

A) Commutative and skew-symmetric
B) Commutative but not skew-symmetric
C) Skew-symmetric but not commutative
D) Neither commutative nor skew-symmetric

Answer 1

The expression (is)⁻¹(i−s)(is)(i−s)⁻¹ is commutative but not skew-symmetric.

Step-by-step explanation:

The expression (is)⁻¹(i−s)(is)(i−s)⁻¹ can be simplified using the commutative and associative properties.

First, let's apply the associative property. We can group the terms as follows: (is)⁻¹((i−s)(is))(i−s)⁻¹.

Next, let's simplify the expression (i−s)(is) using the commutative property. Since the order of the terms changes, we introduce a negative sign. This becomes -sii+s².

Finally, we can group the terms again using the associative property: (is)⁻¹(-sii+s²)(i−s)⁻¹.

Therefore, the expression (is)⁻¹(i−s)(is)(i−s)⁻¹ is commutative but not skew-symmetric.