Question

If matrix A = `[(1, 2),(4, 3)]`, such that AX = I, then X is equal to ______.

Options

• `1/5[(1, 3),(2, -1)]`

• `1/5[(4, 2),(4, -1)]`

• `1/5[(-3, 2),(4, -1)]`

• `1/5[(-1, 2),(-1, 4)]`

Answer 1

If matrix A = `[(1, 2),(4, 3)]`, such that AX = I, then X is equal to `underlinebb(1/5[(-3, 2),(4, -1)]`.

Explanation:

Given, A = `[(1, 2),(4, 3)]`

and AX = I

`\implies` X = A^–1I

`\implies` X = A^–1

Then, A^–1 = `1/|A|[(3, -2),(-4, 1)]`

= `1/(3 - 8)[(3, -2),(-4, 1)]`

= `1/-5[(3, -2),(-4, 1)]`

= `1/5[(-3, 2),(4, -1)]`