# if determinant of a 3*3 matrix A be 6 , then the determinant of matrix B defined by B=5A^2 det(B)= 5^3 * 36 or det(B)=5 *36 ?????

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sciencesolve | Certified Educator

You should use the following property of determinants, such that:

if `det A = a => det (A^2) = a^2`

Hence, since determinant of a matrix is a scalar, multiplying it by another scalar, the result will be the following:

`b*det A = b*a => b*det (A^2) = b*a^2`

Reasoning by analogy yields:

`det A = 6 => det (A^2) = 6^2 => det (A^2) = 36`

`det B = 5*det(A^2) => det B = 5*36`

**Hence, evaluating det B under the given conditions, yields **`det B = 5*36.`