Verify that A2 = I when

We need to prove that: A2 = I = ∵ A = ∴ A2 = By matrix multiplication we have-A2 = ⇒ A2 = ∴ A2 = Hence Verified

Q35 of 146 Page 52

Verify that A² = I when

We need to prove that: A² = I =

∵ A =

∴ A² =

By matrix multiplication we have-

A² =

⇒ A² =

∴ A² =

Hence Verified

If then show that

If and x² = –1, then show that (A + B)² = A² + B².

Prove by Mathematical Induction that (A’)ⁿ = (Aⁿ)’, where n ∈ N for any square matrix A.

Find inverse, by elementary row operations (if possible), of the following matrices.