Question

The inverse of the matrix A = `[(3, 0, 0),(0, 4, 0),(0, 0, 5)]` is ______.

विकल्प

• `[(3, 0, 0),(0, 4, 0),(0, 0, 5)]` 

• `[(1/3, 0, 0),(0, 1/4, 0),(0, 0, 1/5)]`

• `1/60[(1, 0, 0),(0, 1, 0),(0, 0, 1)]` 

• `1/60[(1/3, 0, 0),(0, 1/4, 0),(0, 0, 1/5)]`

Answer 1

The inverse of the matrix A = `[(3, 0, 0),(0, 4, 0),(0, 0, 5)]` is `[(1/3, 0, 0),(0, 1/4, 0),(0, 0, 1/5)]`.

Explanation:

The inverse of diagonal matrix `[(1/"a", 0, 0),(0, 1/"b", 0),(0, 0, 1/"c")]`

∴ The inverse of the given diagonal matrix is `"A"^-1 = [(1/3, 0, 0),(0, 1/4, 0),(0, 0, 1/5)]`