If $A$ is a symmetric matrix and $B$ is a skew-symmetric matrix such that $A+B=\left[\begin{array}{cc}2 & 3 \\ 5 & -1\end{array}\right]$, then $AB$ is equal to :

(B) $\left[\begin{array}{cc}4 & -2 \\ -1 & -4\end{array}\right]$

(A) $\left[\begin{array}{ll}4 & -2 \\ 1 & -4\end{array}\right]$

(C) $\left[\begin{array}{cc}-4 & 2 \\ 1 & 4\end{array}\right]$

(D) $\left[\begin{array}{cc}-4 & -2 \\ -1 & 4\end{array}\right]$

JEE Main · 2019 · 12 Apr 2019 · Shift 1 · Matrices

A

is a symmetric matrix and

B

is a skew-symmetric matrix such that

A + B = [25 3 - 1]

, then

A B

is equal to :

Answer: (B)

Since

A

is symmetric and

B

is skew-symmetric, transposing

A + B = [25 3 - 1]

gives

A - B = [23 5 - 1]

. Adding the two equations,

2 A = [48 8 - 2]

, so

A = [24 4 - 1]

; subtracting,

2 B = [02 - 2 0]

, so

B = [01 - 1 0]

. Multiplying,

A B = [24 4 - 1] [01 - 1 0] = [4 - 1 - 2 - 4]

JEE Main · 2019 · 12 Apr 2019 · Shift 1 · Single correct option