Question

If A = `[(2, x),(0, 1)]` and B = `[(4, 36),(0, 1)]`; find the value of x, given that A² = B.

Answer 1

A² = `[(2, x),(0, 1)][(2,x),(0, 1)]`

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

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

= `[(4, 3x),(0, 1)]`

Given A² = B

`[(4, 3x),(0, 1)] = [(4, 36),(0, 1)]`

Comparing the two matrices, we get

3x = 36

`=>` x = `36/3` = 12