If `A` is `a3x3` matrix, `|A|` `!=` `0` and `|3A|=k|A|` , then write the value of `k` .

Explanation

Since `A` is a `3×3` matrix, A has `3` rows.

`3A` is the matrix obtained by multiplying each entry of A by `3`.

Thus if A has row vectors `a_1​,a_2​ and a_3​.`

`3A` has row vectors `3a_1​,3a_2​ and 3a_3​.`

Since multiplying a single row of a matrix A by a scalar r
has the effect of multiplying the determinant of A by r, we obtain:

`det (3A)=3xx3xx3 `

`det (A)=27 `

`therefore k=27.`