Doubtify – JEE Ki Taiyaari, Simple Bhasha Mein

  ❓ Question The number of singular matrices of order 2 , whose elements are taken from the set { 2 ,   3 ,   6 ,   9 } , is equal to ? 🖼️ Question Image ✍️ Short Solution A 2×2 matrix is singular if and only if its determinant is zero . So the entire question reduces to counting how many choices make the determinant zero . 🔹 Step 1 — Write the general 2×2 matrix Let the matrix be: A = ( a b c d ) where a , b , c , d ∈ { 2 , 3 , 6 , 9 } . 🔹 Step 2 — Condition for singular matrix A matrix is singular iff: ∣ A ∣ = a d − b c = 0 So we need: a d = b c 👉 This is the ONLY condition to check. 🔹 Step 3 — Key observation (MOST IMPORTANT 🔥)** The set: { 2 , 3 , 6 , 9 } has a multiplicative structure : 2 × 3 = 6 , 3 × 3 = 9 , 2 × 6 = 12   ( not allowed ) , 3 × 6 = 18   ( not allowed ) So equality a d = b c ad = bc a d = b c happens only when the ratios match : a b = c d 👉 That means: Either rows are proportional Or columns are proporti...