Given and and and BA = C2, find the values of p and q

Engineering

Mathematics

Algebra of Matrices

Multiplication of Matrices

Question

Given $A = [\begin{array}{cc} p & 0 \\ 0 & 2 \end{array}]$ and $B = [\begin{array}{cc} 0 & - q \\ 1 & 0 \end{array}]$ and $C = [\begin{array}{cc} 2 & - 2 \\ 2 & 2 \end{array}]$ and BA = C², find the values of p and q

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According to question,

BA = C²

[\begin{array}{cc} 0 & - q \\ 1 & 0 \end{array}], [\begin{array}{cc} p & 0 \\ 0 & 2 \end{array}] = [\begin{array}{cc} 2 & - 2 \\ 2 & 2 \end{array}] [\begin{array}{cc} 2 & - 2 \\ 2 & 2 \end{array}]

⟹ [\begin{array}{cc} 0 & - 8 \\ 8 & 0 \end{array}] = [\begin{array}{cc} 0 & - 2 q \\ p & 0 \end{array}]

On compairing quantities,

We, get

– 2q = – 8 and p = 8

⇒ q = 4 and p = 8