Consider the following in respect of the matrices P = [ array ccc 0 & c & -b -c & 0 & a b & -a & 0 array ] and Q = [ array ccc a^2 & a b & a c a b & b^2 & b c a c & b c & c^2 array ] A. PQ is null a matrix. B. QP is an identity matrix of order 3. C. PQ = QP which of the above is/are correct?

Step-by-step solution

We have given, aligned & P = [ array ccc 0 & c & - b - c & 0 & a b & - a & 0 array ], Q = [ array ccc a ^2 & ab & ac ab & b ^2 & bc ac & bc & c ^2 array ] & PQ = [ array lll 0 & 0 & 0 0 & 0 & 0 0 & 0 & 0 array ] and QP = [ array lll 0 & 0 & 0 0 & 0 & 0 0 & 0 & 0 array ] & PQ = QP option ( c ) is correct. aligned