Question

Find the value of x given that A² = B Where A = `[(2, 12),(0, 1)] and "B" = [(4, x),(0, 1)]`

Answer 1

A = `[(2, 12),(0, 1)]` and

B = `[(4, x),(0, 1)]`
A² = B
⇒ A x A = B
⇒ `[(2, 12),(0, 1)][(2, 12),(0, 1)] = [(4, x),(0, 1)]`

⇒ `[(2 xx 2 + 12 xx 0, 2 xx 12 + 12 xx 1),(0 xx 2 + 1 xx 0, 0 xx 12 + 1 xx 1)] = [(4, x),(0, 1)]`

⇒ `[(4 + 0, 24 + 12),(0 + 0, 0 + 1)] = [(4, x),(0, 1)]`

⇒ `[(4, 36),(0, 1)] = [(4, x),(0, 1)]`
Comparing the corresponding elements of two equal matrices, x = 36.