Q. 164.2( 5 Votes )

# A matrix A of order 3 × 3 has determinant 5. What is the value of |3A|?

Answer :

If the determinant of a matrix A of order m is ∆, then the determinant of matrix λA, where λ is a scalar, is λ^{m}∆.

In this question, ∆=5, λ=3 and m=3.

|λA|=3^{3}×5

=135

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PREVIOUSIf I3 denotes identity matrix of order 3 × 3, write the value of its determinant.NEXTOn expanding by first row, the value of the determinant of 3 × 3 square matrix A = [aij] is a11C11 + a12C12 + a13C13, where Cij is the cofactor of aij is the cofactor of aij in A. Write the expression for its value of expanding by second column.

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