Prove that - 3 5- 1 2 - and - 2 -5- -1 3 - are multiplicative inverses to each other-

Now, ([ 3 amp; 5; 1 amp; 2 ]) ([ 2 amp; 5; 1 amp; 3 ]) = ([ 6 5 amp; 15 + 15; 2 2 amp; 5 + 6 ]) = ([ 1 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Inverse of a Matrix

Prove that ...

Question

Prove that $(\begin{matrix} 3 & 5 1 & 2 \end{matrix})$ and $(\begin{matrix} 2 & - 5 - 1 & 3 \end{matrix})$ are multiplicative inverses to each other.

Open in App

Solution

Now, $(\begin{matrix} 3 & 5 1 & 2 \end{matrix}) (\begin{matrix} 2 & - 5 - 1 & 3 \end{matrix}) = (\begin{matrix} 6 - 5 & - 15 + 15 2 - 2 & - 5 + 6 \end{matrix}) = (\begin{matrix} 1 & 0 0 & 1 \end{matrix}) = I$
Also, $(\begin{matrix} 2 & - 5 - 1 & 3 \end{matrix}) (\begin{matrix} 3 & 5 1 & 2 \end{matrix}) = (\begin{matrix} 6 - 5 & 10 - 10 - 3 + 3 & - 5 + 6 \end{matrix}) = (\begin{matrix} 1 & 0 0 & 1 \end{matrix}) = I$
$∴$ The given matrices are inverses to each other under matrix multiplication.

Suggest Corrections

Similar questions

Q. Prove that

A = (\begin{matrix} 5 & 2 7 & 3 \end{matrix})

and

B = (\begin{matrix} 3 & - 2 - 7 & 5 \end{matrix})

are inverses to each other under matrix multiplication.

Q. Find the multiplicative inverse of the following.
(i)

- 13

(ii)

\frac{- 13}{19}

(iii)

\frac{1}{5}

Q. a. Write additive inverse of

\frac{2}{8} a n d \frac{- 6}{- 5}

b. Write multiplicative inverse of

- 13 a n d \frac{- 13}{19}

Q. Find the multiplicative inverse of each of the complex numbers given in the Exercises

11

13

\sqrt{5} + 3 i

$Find the reciprocal (multiplicative inverse) of : (i) \frac{3}{5} \times \frac{2}{3} (i i) \frac{- 8}{3} \times \frac{13}{- 7} (i i i) \frac{- 3}{5} \times \frac{- 1}{13}$

Join BYJU'S Learning Program

Prove that (3512) and (2−5−13) are multiplicative inverses to each other.

Now, (3512)(2−5−13)=(6−5−15+152−2−5+6)=(1001)=IAlso, (2−5−13)(3512)=(6−510−10−3+3−5+6)=(1001)=I∴ The given matrices are inverses to each other under matrix multiplication.

Prove that $(\begin{matrix} 3 & 5 1 & 2 \end{matrix})$ and $(\begin{matrix} 2 & - 5 - 1 & 3 \end{matrix})$ are multiplicative inverses to each other.