JEE Main 2015 · 4 Apr · Shift 1 · Mathematics Q64

← JEE Main 2015 · 4 Apr · Shift 1

MathematicsSingle correct+4 / -1Question 64 of 90

If $A=\begin{bmatrix}1&2&2\\2&1&-2\\a&2&b\end{bmatrix}$ is a matrix satisfying the equation $AA^T=9I$ , where I is 3×3 identity matrix, then the ordered pair (a, b) is equal to :

(2, −1)

(−2, 1)

(2, 1)

(−2, −1)

Answer and worked solution

Official answer: D

The rows of $A$ must be orthogonal:

Row 1 · row 3: $a+4+2b=0$ .
Row 2 · row 3: $2a+2-2b=0$ .

So $a=b-1$ and $3b+3=0$ : $b=-1$ , $a=-2$ . Also $a^2+4+b^2=9$ ✓.

Topics:Special matrices

← Previous question Next question →

JEE Main 2015 · 4 Apr · Shift 1, Mathematics question 64