Verifying properties of a determinant

Chapter 4 Class 12 Determinants
Concept wise

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Question 15 Choose the correct answer. Let A be a square matrix of order 3 Γ 3, then |"kA" | is equal to A. "k" |"A" | B. "k" 2|"A" | C. "k" 3|"A" | D. 3"k" |"A" | Let A = [β 8(π1&π1&π1@π2&π2&π2@π3&π3&π3)]_(3 Γ 3) We need to find |kA| kA = k [β 8(π1&π1&π1@π2&π2&π2@π3&π3&π3)] = [β 8(ππ1&ππ1&ππ1@ππ2&ππ2&ππ2@ππ3&ππ3&ππ3)] If a matrix is multiplied by a constant, then constant is multiplied to all elements of matrix |"kA" | = |β 8(ππ1&ππ1&ππ1@ππ2&ππ2&ππ2@ππ3&ππ3&ππ3)| Taking out k common from R1 R2 & R3 = k. k. k |β 8(a1&b1&[email protected]&b2&[email protected]&b3&c3)| = k3 |β 8(a1&b1&[email protected]&b2&[email protected]&b3&c3)| = k3 |A| Thus, Correct answer is C Property: If each element of row of determinant is multiplied by a constant k , then its value get multiplied by k